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^d?Aaviiaiii^ 


GRADED   LESSONS 

IN  HARMONY 


BY 

F.    H.   SHEPARD 

(Revised  and  Prepared  by 
A.  Agnes  Shepard  and  Florian  A.  Shepardj 


Mr.  Shepard  is  the  Author  of  "Harmony  Simplified."    "Children's 
Harmony,"    "How  to   Modulate,"    "Piano-Touch   and 
Scales,"   "Church  Music  and  Choir-Train- 
ing," "Keyboard  Diagram,"  Etc. 


NEW    YORK 

G.  SCHIRMER,  INC. 

3   East  43d  Street 

1914 

4-0  ^-^\ 


Copyright,  1914,  by  G.  Schirmer.  Inc. 

All  Rights  Reserved 
Entered  at  Stationers'  Hall,  London 


Rlanchard  Pres-i 

Isaac  H.  Blanchard  Company 

New  York 


K-'1  T 


FRANK    H.    SHKPARD 


BIOGRAPHICAL  SKKTCH 

OF 

FRANK  II.  SHEPARD 


I'lank  II.  Shepard  was  born  in  Bethel,  Conn.,  in  1863. 
At  the  age  of  fourteen  he  invented  a  machine  by  which  he 
was  enabled  to  earn  the  money  for  a  musical  echication.  This 
invention.  simpHfying  the  process  of  cloth  production,  was 
prophetic  of  his  later   discoveries  in   Music. 

From  1880  to  1884  he  studied  organ  with  Eugene  Thayer 
and  others  in  Boston  and  New  York ;  did  concert  organ  work 
at  the  Great  Hopkins  (Roosevelt)  Organ  in  Great  Barrington, 
Mass.;  organized  Boy  Choir  at  Trinity  Cathedral,  Cleveland. 

As  a  foundation  for  his  original  researches,  Mr.  Shepard 
enjoyed  the  instruction  of  leading  American  and  European 
teachers,  including  nearly  four  years  (1885-1889)  at  the  Leip- 
zig Conservatorj^  under  Bruno  Zwintscher  and  Dr.  Paul  for 
piano;  Homeyer,  the  Gewandhaus  organist;  Dr.  Jadassohn  for 
harmony,  counterpoint,  canon  and  fugue ;  Herr  Gustav 
Schreck  for  free  composition  and  form ;  and  Torrsleff  for 
voice. 

In  1889  he  published  Hov:  to  Modulate  in  which  is  pre- 
sented the  principle  of  "Attendant  Chords,"  which  gives  a 
deeper  insigiit  into  the  mysteries  of  Musical  Structure,  and  a 
working  knowledge  in  more  different  directions  than  any  other 
single  detail  of  Musical  Theory.  Not  only  does  it  supply  a 
simple,  comprehensive  plan  for  modulation,  but  it  is  equally 
essential  in  analysis,  improvisation,  transposition  and  the 
understanding  of  many  foreign  chords,  like  those  at  the  begin- 
ning of  Mendelssohn's  "Wedding  March,''  or  throughout  his 
"Spring  Song."  The  book  also  contains  the  "Principle  of 
Artistic  Modulation." 

In  1890  appeared  Piano  Touch  and  Scales,  containing  prol)- 
ably  tiie  first  presentation  of  the  principle  of  relaxation.  In 
the  same  year  came  Church  Music  and  Choir  Training,  giving 
him  a  standing  as  an  authority  upon  the  training  of  the  lioy 
voice  and  management  of  boy  choirs. 

iii 


IV  Graded   Lessons    in    Ilarmoni/ 

In  1891  TIic  ShcpaiJ  School  of  Music  was  cstablibhcd  at 
Orange,  K.J.  The  large  three  manual  concert  pipe  organ 
(Hutchings),  now  in  the  Recital  Hall,  was  erected  chiefly  bj^ 
]\Ir.   Shepard's  own  hands  and  completed  in   December,   1912. 

In  1896  Harnwny  Simplified  was  published.  Presenting  so 
much  that  was  new,  both  in  principle  and  practice,  this  book 
was  a  most  daring  venture ;  the  positions  taken  in  the  book 
proved  unassailable,  no  word  of  opposition  ever  reaching  its 
author;  and  its  unprecedented  sale  among  modern  works  of 
its  class  is  significant  of  popular  approval.  Mr.  Shepard  has 
made  several  valuable  contributions  to  the  science  and  peda- 
gogy of  musical  theory,  contributions  in  the  line  of  simplifica- 
tion and  systematic  grouping.  One,  of  the  highest  importance 
to  students,  is  his  grouping  of  the  seven  most  difficult  chords 
of  nnisic  in  one  class,  showing  how  they  are  all  forms  of  one 
and  the  same  chord  principle.  By  this  method  even  the  chords 
of  the  Augmented  Si.xth,  which  have  always  been  a  bone  of 
contention  among  authorities  on  composition,  become  abso- 
lutely simple  both  to  form  and  to  recognize.  To  understand 
the  inner  meaning  and  qualities  of  the  chord  of  the  Dominant 
S'eventh,  which  Mr.  Shepard  shows  as  a  foundation  principle, 
leads  directly  to  the  understanding  of  the  structure  and  use 
of  the  more  complicated  forms,  such  as  the  Diminished  Sev- 
enth, Dominant  Ninth  and  the  three  forms  of  the  Augmented 
Sixth  chord.  The  principle  involved,  though  simple,  is  prac- 
tically universal  in  its  application. 

In  1899  appeared  the  Keyboard  Diagram. 

In  1901  Mr.  Shepard  began  teaching  Harmony  by  Corre- 
spondence. 

1906  saw  the  formal  launching  of  the  Shepard  Piano  Sys- 
tem by  Mail.  The  finding  of  the  power  of  mental  vitaliza- 
tion,  the  rapid  unfoldment  of  other  principles  from  this,  and 
the  crystallization  into  a  distinctive  system,  make  it  worthy  of 
a  distinctive  name.  As  evidenced  bj^  the  spontaneous  expres- 
sions of  students  from  all  parts  of  the  world,  the  Shepard 
Piano  System  is  a  new  force  in  music  study  and  teaching. 

i\Iany  of  the  advances  made  in  the  piano  work  are  of  the 
deepest  significance,  and  when  collected  and  applied  in  a  logi- 
cal, comprehensive  system  they  form  an  epoch-making  event 
in  the  development  of  the  science  of  piano  teaching  and  study. 
To  Mr.  Shepard's  mind  the  work  he  accomplished  in  Harmony 
had  not  one-tenth  of  the  value  possessed  by  his  piano  work, 
which  was  the  result  of  twenty  years  of  search  and  study,  of 
experiment  and  discovery;  and  this,  together  with  his  promul- 


(Iradcd    TjI'ssoiis    in    Ilaitno)!//  v 

yatioii  of  so  many  (li.slincli\  c,  (li\cTsc  and  iiiiporlanl  advances, 
made  him  many  grateful  and  warm  friends  all  over  the 
world. 

The  years  1907-9  were  partly  devoted  to  the  planning  and 
partial  writing  of  l)ooks  on  Ear-fraiuiiig,  Sight  Singing  and 
Trausf^osition. 

In  1908  /]  Key  to  Ilaruiony  Simplified  and  a  Classrooiii 
Manual  was  puhlishcd.  This  was  the  result  of  long  years  of 
experience  in  the  teaching  of  classes  and  individuals,  and  is 
in  large  measure  a  systematic  compilation  of  personal  notes 
to  pupils,  together  with  the  best  solutions  (and  explanations) 
of  the  exercises  assigned  in  Harmony  Simplified. 

During  the  last  years  of  his  life,  and  especially  after  the 
publication  of  the  Key,  until  his  deatli  in  February,  1913,  Mv. 
Shepard  devoted  his  best  time  and  attention  to  the  comple- 
tion of  the  Shepard  Piano  System.  This  work,  considered  by 
its  author  as  by  far  his  greatest  achievement,  was  given 
permanent  form  in  the  shape  of  a  Correspondence  Normal 
Course — a  form  such  that  it  may  be  easily  imparted  and 
spread  among  all  earnest  musicians.  By  an  almost  superhuman 
effort  just  before  his  death,  Mr.  Shepard  gave  to  this  Piano 
Xormal  Course  its  finishing  touches;  and  the  nearly  simul- 
taneous completion  of  this  system  and  of  the  home  organ, 
the  one  a  symbol  of  his  work,  the  other  of  his  play — for 
mechanics  fascinated  him  as  intensely  as  music  inspired  him — 
formed  the  culmination  of  a  life  devoted  to  simplifying  and 
broadening  musical  principles  and  to  stimulating  musical 
ideals. 


PREFACE 


I\Ir,  Frank  II.  Shepard,  as  teacher  and  pedagogue,  re- 
ceived such  enthusiastic  commendations  and  spontaneous 
expressions  of  help  and  delight  from  those  pursuing  his 
Correspondence  Harmony  Course,  that  it  seems  imperative 
to  present  these  lessons,  together  with  his  personal  notes 
and  suggestions,  in  book  form.  To  those  who  know  Har- 
mony Simplified  it  is  hardly  necessary  to  say  simplicity, 
ihoroiighncss  and  practical  application  characterize  the 
contents  of  the  lessons  contained  in  this  volume. 

The  first  lessons  reveal  the  "Laws  of  Relationship,"  the 
real  foundation  of  musical  structure  and  the  source  of  the 
"'rules."  Part-writing  becomes  absorbingly  interesting, 
because  principles  are  used  instead  of  rules.  The  Key- 
board Drill  is  unique  and  of  great  help  to  piano  teachers 
and  students,  as  is  the  Ear-training. 

These  lessons  are  designed  to  help  teachers  to  teach 
Harmony  in  a  simple  and  practical  manner,  having  fully 
as  much  reference  to  the  needs  of  the  performer  as  to 
those  of  the  composer.  It  provides  the  teacher  with  de- 
lightful material  for  class  talks,  lectures  and  scientific 
jjresentation  of  the  subject  in  a  logical  manner. 

This  work  supplies  a  new  and  vital  element  in  musical 
culture.  It  is  not  Harmony  study  alone,  as  generally 
understood,  for  it  differs  in  many  respects.  Some  of  its 
unique  features  are : 

(1)  Keyboard  JVork.  In  order  to  make  the  work 
practical  for  teachers  and  performers,  much  attention  is 
given  to  the  formation  and  use  at  the  keyboard,  of  the  va- 
rious Intervals,  Chords,  Cadences  and  other  progressions 
including  also  Improvising,  Modulating  and  Transposing. 
With  the  aid  of  the  Keyboard  Diagram  this  also  becomes 
possible  in  Plarmony  class  work. 


'   ii  (ifddcd    Lessons    in    Ilarmom/ 

(2)  The  RcpUici)i(j  of  the  N iiiiibcrlcss  Rules  for  Part- 
writing  by  a  few  broad  principles,  which  explain  both 
rules  and  exceptions. 

(3)  The  Classification  of  the  Chords  of  the  Dominant 
Seventh,  Major  and  Minor  Ninth,  Diminished  Seventh  and 
the  three  forms  of  the  Augmented  Sixth,  as  only  slightly 

DIFFERING  FORMS  OF  ONE  AND  THE  SAME   HARMONY,  simpli- 
fying wonderfully  these  more  complicated  chords. 

(4)  "The  Principle  of  Tendencies,"  which  explains 
many  of  the  perplexing  things  in  Musical  Theory,  and 
simplifies  the  subject  wonderfully. 

(5)  The  "Attendant  Chords,"  which  make  many  for- 
eign harmonies  clear. 

(0)  Modulation,  presented  in  a  very  simple  and  prac- 
tical form. 

(7)  Studies  in  Analysis  and  Ear-training,  with  hints 
on  Improvising. 

(8)  The  Knoidedge  of  the  Underlying  Principles  of 
Acoustics,  Musical  Structure  and  Tone  Relations,  which 
explain  most  of  the  mysterious  things  about  which  many 
trained  musicians  are  unenlightened. 

(9)  The  Use  of  the  "Sharpest  Note''  as  a  means  of 
analyzing  foreign  chords,  which  is  a  revelation  to  most 
musicians. 

The  earnest  student  will  find  that  the  faithful  study  of 
these  lessons  will  build  a  practical  musicianship ;  will  give 
the  power  to  do  things  at  the  keyboard;  to  hear  and  to 
think  music;  to  analyse,  to  modulate  and  to  improvise. 
The  study  should  not  only  teach  him  much  that  he  wishes 
to  know,  but  should  broaden  him  mentally  and  musically. 
This  work  goes  right  to  the  heart  of  music. 

I  take  pleasure  in  acknowledging  my  indebtedness  in 
this  work  to  a  number  of  friends:  in  particular,  to  Mr. 
Isaac  H.  Blanchard,  my  constant  counsellor,  for  courte- 
sies, personal  and  professional,  in  aid  of  my  labor  now 
ended;  and  to  numerous  correspondence  pupils  of  Mr. 
Shepard  and  myself,  who  by  their  deep  interest  and 
thoughtful  questions  have  stimulated  further  thought  and 
have  pointed  out  oi)|)ortunitics  for  the  clearer  expression 
of    ideas   alrcadv    tornudated.      I^ir    much    time   and    care 


Graded   Lessons    in    Ihirmonji  ix 

spent  in  revising  manuscripts,  verifying  references  and 
footnotes,  and  correcting  proof  sheets  of  the  present  work, 
as  well  as  for  valuable  suggestions  during  its  preparation, 
I  am  grateful  beyond  my  power  of  expression  to  Miss 
Violet  L.  Jacquin,  whose  personal  connection  with  Mr. 
Shepard  for  more  than  eight  years  has  rendered  her 
sympathetic  cooperation  invaluable. 

A.  Agnes  Shepard  (]\Irs.  F.  H.), 
Director  of  Shepard  School  of  Music, 

Orange,  N.J. 
September,   1914. 


CONTENTS 


Lessons  1-4,  §§1-42*.  Scales.  Material  for  study— The  Ma- 
jor scale  as  a  principle — The  Minor  scales — Signatures — 
Related  keys — The  Chromatic  scales — The  office  of  the 
half-step — Principle  of  Melodic  Tendencies — The  meaning 
of  Scale  Relationships — Keyboard  exercises — Written 
exercises — Ear-training — Drills— Questions  and  answers — 
Collateral  reading  and  suggestive  notes. 

Lessons  5-8,  §§43-68.  Intervals.  Material  for  study— Gen- 
eral names — Specific  names — Measurement  of  intervals — 
Inversions — Consonant  and  dissonant  intervals — Disso- 
nant intervals  that  sound  well — Difference  between  Major 
and  Perfect  intervals — Keyboard  exercises — Drills — 
Written  exercises — Ear-training — Questions  and  answers 
— Collateral  reading — Suggestive  notes — Daily  technique 
drill   in   theory. 

Lessons  9-13,  §§69-99.  Triads.  Material  for  study— The 
principle  of  chord  building— The  alternate  letter  principle 
— Chord  structure  in  general — The  material  of  music,  or 
the  scale  as  the  basis  of  all  music — The  specific  forms  of 
triads:  Major,  Minor,  Diminished  and  Augmented — About 
the  term  position — Improvisation — Bounding  and  Rocking 
chords — Inversions — Principal  and  secondary  triads — 
Doubling— Figuring— Keyboard  and  written  exercises- 
Special  drills— Methods  of  practice— Recitations— Variety 
of  drill— Ear-training— Questions  and  answers— Collateral 
reading — Important  notes. 

Lessons  14-18,  §§100-116.  Part-writing-^Triads.  Material 
for  study — Connection  of  triads  in  simplest  form — To 
connect  triads  when  there  is  no  common  note — How  to 
discover  Consecutive  Fifths  and  Octaves  in  written  work- 
To  avoid  the  Augmented  Second  from  6  to  7  of  the  Minor 
scale— Concerning  the  rule  which  requires  the  common 
note  to  remain  in  the  same  voice — How  to  choose  be- 
tween two  possible  progressions — Hidden  Fifths  and  Oc- 
taves— Broken  chords— Chord  individuality— Correlative 
character  of  different  chord  forms — Transposition— Key- 
board and  written  exercises — How  to  use  the  /Cry- Ques- 
tions—Collateral  reading— Observations  and  special  notes. 

*  Numbers  refer  to  paragraphs. 


Graded  Lessons  in  Ilarmovi/  xi 

Lessons  19-23,  §§117-150.  Chords  of  the  Seventh.  Material 
for  study— Construction— Positions  —  Inversions  —  Com- 
bining the  various  positions  and  inversions— Figuring — 
Consonance  and  Dissonance  as  a  principle — The  principle 
of  Tendencies — The  principle  of  Fiesolution— Practical 
application — The  closing  formula — Keyboard  and  written 
exercises— Drills— Observations  and  notes — Questions  and 
answers— Ear-training— Important  collateral  reading  and 
observations. 

Lessons  24-26,  §§151-158.  Part-writing  — Dominant  Seventh 
Chord.  Material  for  study— The  principles  of  Part- 
writing — The  principle  of  Harmonic  Tendencies — Special 
directions,  hints,  etc.— Perception  of  music  through  hear- 
ing— Keyboard  and  written  exercises — Questions — Ear- 
training — Xotes  on  advanced  part-writing — Collateral 
reading. 

Lesson  27,  §159.  Cadences, — Elaborated  Melodically.  Ma- 
terial for  study— Passing  notes— Improvisation— Key- 
board and  written  exercises. 

Lesson  28,  §160.  Harmonizing  the  Scale.  Material  for  study 
— Written  exercises. 

Lessons  29-33,  §§161-172.  Part-writing— Secondary  Seventh 
Chords.  Material  for  study — Resolutions— Exercises  witii 
non-cadencing  resolutions — Keyboard  and  written  exer- 
cises—Questions— Ear-training— Collateral  reading— Har- 
monizing the  scale — Analytical   and  comparative  reviews. 

Lesson  34,  §§173-176.  Introduction  to  Modulation.  Material 
for  study — Modulation  to  Sui)-dominant — To  relative 
Minor— Relative  sharpness  of  scale  tones— Processes— 
Formula— Keyboard  and  written  exercises— Notes. 

Lesson  35,  §§177-180.  Attendant  Chords.  Material  for  study 
— Preparation  for  modulation  and  analysis — Keyboard 
and  written  exercises — Questions — Xotes. 

Lesson  36,  §§181-185.  Modulation— Use  of  Attendant  Chords. 
Material  for  study — Treatment  of  bass  in  inverted  chords 
— Drill— Keyboard  and  written  exercises— Remarks— Har- 
monizing the  scale. 

Lessons  37-38,  §§186-191.  Chord  Analysis.  Material  for 
study — Analysis  of  hymn  tunes — Detailed  process — .Analy- 
sis of  piano  music— Passing-notes— Material  for  analysis. 


xii  Graded  Lessons   in   Ilarmuni/ 

Lessox  39,  §§192-198.  Chord  of  the  Dominant  Seventh  and 
Ninth.  Material  for  study — Inversions — Preparation  of 
dissonances — Keyboard  and  written  exercises — Drills — 
Questions — Ear-training. 

Lessons  40-42,  §§199-215.  Chord  of  the  Diminished  Seventh. 
Material  for  study — Inversions — Study  of  roots  and  nota- 
tion— To  discover  the  key  in  which  a  foreign  fundamental 
chord  is  written — To  proceed  from  the  chord  of  the 
Diminished  Seventh  to  any  one  of  the  twelve  Major  and 
twelve  Minor  keys — Keyboard  and  written  exercises — 
Drills — Notes  and  observations— Questions — Harmonizing 
the  scale. 

Lessons  43-44,  §§216-225.  Chords  of  the  Augmented  Sixth 
Material  for  study— The  Augmented  Six-three  chord— 
the  Augmented  Six-four-threc  chord — The  Augmented 
Six-five-three  chord — Attendant  chords  may  appear  in 
the  form  of  the  Augmented  Sixth  chord — Keyboard  and 
written  exercises — Questions — Harmonizing  the  scale. 

Lessons  45-47,  §§226-230.  Modulation.  Material  for  study- 
New  tonality  is  thoroughly  established  by  addition  of  the 
closing  formula — Ways  and  means  of  modulating — Drills 
— Keyboard  and  written  exercises — Questions. 

Lessons  48-49,  §§231-237.  Altered  Chords.  Material  for 
study — Keyboard   and   written    exercises — Questions. 

Lessons  50-54,  §§238-253.  Pasring-notes— Suspensions.  Ma- 
terial for  study — Keyboard  and  written  exercises— Ques- 
tions. 

Lessons  55-56,  §§254-266.  Chord  Analysis  (Cont.).  ^laterial 
for  study — Analysis — Drill  in  transposing  hynm  tiines  into 
the  four  clefs  and  in  reading  orchestral  music — Keyboard 
and  written  exercises — Questions. 

Lessons  57-60,  §§267-285.  Harmonizing  Melodies.  Material 
for  studv— Review — Exercises  in  transposition,  in  writing 
and  at  the  keyboard— Original  harmonization— Original 
examples  of  hymn  tunes  and  plirases  written  in  free  form 
for  piano. 

Lesson  61,  §286.  Analysis  and  Form.  Material  for  study- 
Exercises. 


Remarks  and  Suggestions 


The  plan  of  this  work  is  to  carry  on  simultaneously 
several  different  lines  of  training,  to  secure  not  only  a 
knowledge  of  Harmony,  but  also  of  other  related  subjects, 
insuring  a  broad  and  useful  culture  in  Music.  Included 
in  the  course  are:  (1)  Constructive  work  at  the  key- 
board, which  is  the  most  helpful  training  ever  devised  for 
the  praetical  )iuisician;  (2)  Harmony  study  proper,  but 
with  Principles  substituted  for  Arbitrary  Rules,  and  many 
new  practical  features;  (3)  x^nalysis;  (4)  Ear-training; 
(5)    Part-writing  and  Composition. 

In  the  preparation  of  each  lesson  the  student  should 
thoughtfully  study  the  matter  assigned,  writing  down 
every  question  or  observation  that  may  occur.  He  will 
then  do  the  exercises,  many  of  which  may  be  done  at 
keyboard.  In  some  lessons  will  be  found  a  series  of  test 
questions  to  be  answered  in  writing.  These  answers, 
with  the  written  exercises  and  the  record  of  the  keyboard 
exercises,  together  with  incidental  questions,  might  con- 
stitute a  recitation.  This  lesson  should  be  corrected, 
further  test  questions  given  to  cover  any  weak  points 
revealed  by  the  recitation,  and  the  advance  lesson  as- 
signed. 

Each  lesson  is  designed  to  take  from  three  to  live 
hours  in  preparation,  including  the  Keyboard  Drill  and 
Ear-training.  Do  not  consider  a  lesson  complete  when 
you  have  answered  the  questions  and  studied- the  subject 
matter.  P^uUy  one-half  of  the  time  should  be  spent  on 
keyboard  and  other  drill. 

Systematic  work  is  essential  to  real  success. 

Remember  that  in  all  this  work  the  underlying  thought 
and  the  principles  involved  are  of  the  first  importance. 
Many  students  think  they  have  the  whole  matter  when 
they  have  written  the  exercises  (without  thought),  or 
have  answered  the  questions  without  realizing  the  rela- 
tionship to  the  foundation  principles. 

Facility  in  doing  is  just  as  necessary  as  knowledge. 
The  exercises  are  designed  to  give  this  facility  and  to 
teach  you  to  think  musically  either  at  the  keyboard  or 
away   from   it. 

Courage!  Always  approach  your  study  with  the 
thought,  /  idll,  not  i  wish  I  could. 


'Untwisting   all   the   chains    that   tie 
The  hidden  soul  of  Harmony." 

— Milton. 


THE    SHEPARD 

GRADED   LESSONS 

IN  HARMONY 


Note:  Those  using  this  volume*  in  teaching  or  for  self- 
instruction  will  find  it  necessary  to  have  a  copy  of  Har- 
mony Simplified**  and  one  of  A  Key  to  Harmony  Simpli- 
fied'and  a  Classroom  Manual***  by  F.  II.  Shepard. 


LESSON  I 

]\IoTTO — Not  only  Knowledge,  but  also  Facility  is  to  be 

attained. 

Let  these  Tivo  Points  control  your  study. 

SCALES 

The  Major  Scale  As  a  Principle. 

1.  STUDY. 

Read  daily  for  one  week  Harmony  Simplified,  §§1-35, 
45.     Also,  Collateral   Reading  and  Suggestive  Notes  §12. 

2.  KEYBOARD  EXERCISES. 

(1)   Form  Half-steps  and  Whole-steps  from  any  and 
every  note,  as  described  in  H.  S.,  §1.     N.B. — In  teaching 

*  Paragraphs  in  The  Shepard  Graded  Lessons  in  Harmony  are  referred 
to  as  g  — . 

**  Paragraphs  in  Harmony  Shnplified  are  referred  to  as  H.  S..  ?  — . 

***  Key  — ,  refers  to  sections  in  .1  Key  to  Harmony  Simplified  and  a  T/nyj- 
room  Manual. 

I 


2  Graded   Lessons   in   Ilannoni) 

children,  this  point  should  receive  ample  drill  before  con- 
structing the  scales. 

(2)  Learn  to  number  the  degrees  of  any  scale.  {H.  S., 
§§  2-6.) 

(3)  Form  the  scales  G,  D,  A,  E,  B,  F-sharp  and 
C-sharp,  numbering  the  degrees  as  you  touch  the  cor- 
responding keys,  and  observing  the  steps  and  half-steps. 
Note  any  difficulties.  If  you  are  not  sure  of  the  note^ 
you  may  write  the  scales  before  playing  them. 

(4)  Form  similarlv  the  double-sharp  scales.  (See 
H.  S.,  §7.) 

(5)  Form  similarly  the  scales  in  flats.   (See  H.  S.,  §8.) 

(6)  Form  similarly  the  double-flat  scales.  (See  H.  5"., 
§9.) 

3.  SPECIAL  NOTE. 

For  this  first  lesson  it  is  more  important  to  find  the 
principles  involved — to  discover  the  inner  meaning  of  the 
scale  relations — than  to  have  a  recitation  that  is  perfect. 
Sometimes  pupils  think  that  this  lesson  is  so  easy  that  it  is 
simply  something  to  be  "gotten  over  with"  as  soon  as 
possible,  and  they  are  surprised  enough  to  discover  the 
true  beauty  and  the  deep  principles  involved.  The  chief 
point  of  the  lesson  is,  then,  not  the  correct  writing  of  the 
scales,  but  the  discoz'ery  of  the  underlying  thought. 

4.  WRITTEN  EXERCISES. 

(1)  Following  the  pattern  shown  in  Fig.  5  of  H.  S., 
drawing  the  line  from  5  down  to  1  of  the  next  scale, 
write  the  above  named  Major  scales.  X.B. — At  the  end 
of  each  scale,  and  on  the  same  staff,  draw  a  double  bar 
and  then  write  the  signature,  taking  it  from  the  scale 
as  shown  in  H.  S.,  §12. 

5.  RECITATION. 

(Recite  to  yourself  or  to  a  friend.) 

(1)  Without  seeing  a  keyboard,  test  as  to  the  steps 
and  half-steps  above  and  bclozv  any  and  every  note. 

(2)  Recite  the  notes  of  the  scale;  that  is,  taking  any 
given  scale,  simply  name  the  notes  as  they  occur,  not 
forgetting   the    sharps   or   flats.      If   unfamiliar  with   the 


Graded   Lessons    In    Flarmoni/  3 

scales  you  may  follow  the  wording  shown  in  //.  S., 
§4;  but  if  able,  you  need  simply  mention  the  notes 
alone.  For  example,  the  notes  of  the  scale  of  B  are 
B,  C-sharp,  D-sharp,  E,  F-sharp,  G-sharp,  A-sharp,  B. 
If  not  too  difficult  for  you,  let  this  exercise  include  the 
double-sharp  and  double-flat  scales.  Use  the  metronome 
to  test  the  speed  you  attain,  naming  one  note  to  each  beat. 

G.     EAR-TR.\IXIXG. 

Read  H.  S.,  §§47-50.  See  also  the  special  Ear-training 
Exercises,  §11. 

(1)  Try  to  sing  (or  hum  or  whistle)  half  and  whole 
steps  above  and  below  given  notes  upon  the  piano.  Prove 
by  playing  the  note  after  singing  it. 

(2)  Practice  1-5  of  the  Ear-training  Exercises. 
N.B. — Ear-training  is  not  obligatory,  but  of  extreme  value, 
and  is  recommended. 


7.  QUESTIONS.* 

Commence  to  write  the  answers  after  a  day  or  two 
of  study. 

Note.  Advanced  students,  if  they  feel  quite  sure  they 
have  nothing  to  learn  about  scale-writing  or  key-relation- 
ships, need  write  only  two  scales  each,  in  sharps,  flats, 
double-sharps  and  double-flats.  Even  if  they  understand 
the  matter  themselves,  they  may  gain  a  point  about  how 
to  teach  others. 

(1)  Where  are  the  half-steps  in  the  Major  scale? 

(2)  State  two  or  three  foundation  principles  covering 
its  construction. 

(3)  For  what  are  sharps  usedPf     Also  double-sharps? 

(4)  How  many  kinds  of  Major  scales  are  there,  and 
why  ? 

(5)  For  what  are  flats  and  double-flats  usedPf 

(6)  What  is  a  signature  ?f     Give  its  origin. f 

(7)  State  the  order  of  sharps  in  the  signature;  of  flats. 

*  For  best  results  write  orifjin.-il  answers  to  these  fiiiestions  before  reading 
those  Riven  below. 

t  But  few  rcaih  the  iinderlyint;  thouuht  in  these  questions. 


4  Graded  Lessons   in   Harmony 

(8)  Describe  Tetrachords  and  their  office  in  the  order 
of  keys.* 

(9)  Give  the  order  of  scales  with  sharps;  also  with 
flats. 

(10)  What  is  the  difference  between  a  scale  and  a 
key  ?t 

8.  ANSWERS. 

(1)  The  half-steps  in  the  ]\Iajor  scale  are  from  3  to  4 
and  from  7  to  8.  This  is  a  law,  because  it  represents  a  fixed 
relationship.  A  short  formula  for  scale-construction  is : 
"The  half-steps  are  from  3  to  4  and  from  7  to  8.  All  other 
steps  are  whole-steps."     Let  your  pupils  memorise  this. 

(2)  (I)  Do  not  write  two  notes  upon  the  same  degree  of 
the  staff.  (IT)  Do  not  skip  any  letter.  In  other  words,  the 
letters  must  be  used  consecutively,  else  it  is  not  a  scale.  See 
H.  S.,  §5. 

(3)  When  we  look  deeply  for  the  real  principles,  we  see 
that  sharps  and  flats  (also  double-sharps  and  double-flats) 
are  used  primarily  and  originally  to  make  the  scales  alike  or 
to  represent  THE  scale,  i.e.,  the  scale  principle,  at  any  and 
all  pitches. 

(4)  There  is  ONLY  OXE  KIXD  of  i\Iajor  scale,  since  the 
different  so-called  scales  are  merely  duplicates  of  the  one 
scale  principle  at  different  pitches,  that  is,  in  different  keys. 
Many  people  think  that  the  scale  of  Ab  is  a  different  kind  of 
scale  from  the  scale  of  D,  for  example ;  but  a  melody,  or 
musical  thought,  can  be  represented  just  as  zvell  in  one  as  in 
the  other. 

(5)  For  the  same  reason  as  with  sharps — to  make  the 
scales  alike;  or  to  represent  the  one  Major  scale  principle. 

(6)  This  question  is  more  frequently  missed  than  almost 
any  other,  for  but  few  see  the  connection  betivecn  the  scale 
and  the  signature.  The  answer  is :  "\  signature  is  the  col- 
lected sharps  or  flats  used  in  forming  the  scale.  Its  source 
is  in  the  scale  or  in  its  uniform  construction."  Signatures 
come  from  the  scale — not  vice  versa.  See  how  the  scale 
and  its  relationships  are  the  true  foundation,  not  only  of 
music,  but  of  its  notation  as  well.  Also  see  this  point  later 
in  the  notation  of  chords. 

(7)  The   order   of    sharps   is:    FJ,    CJ,    Gt,   DJf,    Aft,    Ftt, 


*  But  few  reach  the  underlyine;  thoiiKht  in  tliose  qupstions. 
t  These  questions  are  dcsignofl  to  stimulate'  ori^^inal  thought. 


(haded  Lessons   in   Harmon  1/  5 

Tlie  order  of  flats  is;  P.b,  Eb,  Ab.  Db.  Gb  Cb,  Fb. 
Observe  that  one  is  the   exact  reverse  of  tlie  other,  and 
tell  why,  if  you  can. 

(8)  Tetrachords  are  scales  of  four  tones  which  come 
from  an  old  Greek  form.  They  might  be  described  in  our 
notation  as  half -scales,  since  we  find  in  each  Major  scale  two 
Tetrachords,  one  placed  above  the  other.  Their  office  in  the 
order  of  kevs  is  most  important,  as  they  explain  some  of 
the  most  important  matters  in  related  keys  and  in  musical 
form.  As  each  key  or  scale  is  related  through  its  two  Tetra- 
chords to  the  scale  having  one  vwre  sharp,  on  the  one  hand, 
and  to  the  scale  having  one  less  sharp,  on  the  other  hand,  we 
have  at  once  the  famibar  group  of  the  three  keys  called  the 
Tonic,  Dominant  and  Sub-dominant. 

(9)  The  order  of  scales  with  sharps  is  G,  D,  A,  E,  B, 
Yt,  Ct. 

'The  order  of  scales  with  flats  is  F,  Bb,  Eb,  Ab,  Db,  Gb,  Cb. 
Can  you  repeat  the  above  quickly,  and  state  the  number  of 
sharps  or  flats  in  each  key? 

(10)  The  "scale"  implies  the  regular  succession  of  the 
7  (or  8)  tones;  while  '7>'(\v"  implies  the  same  relatiuiishits, 
but  with  no  particular  order  required.  In  both  scale  and 
key  notice  that  relationship  of  tones  is  implied,  or  the  choice 
of  tones  having  fixed  relations  to  each  other.  Remember 
that  relationship  is  the  great  foundation  of  music  and  the 
original  source  of  all  its  laws.  (Think  deeply  on  this  last 
statement.) 

9.  NOTE  ABOUT  DOUBLE-SHARPS  AND  DOUBLE- 
FLATS  IN  THE  SIGNATURE. 

It  is  not  customary  to  use  double-flats  or  double-sharps 
in  the  signature,  although  I  do  not  recognize  any  reason 
why  they  cotdd  not  be  used.  At  present  it  seems  to  be 
the  idea'  to  express  the  key  in  the  most  simple  manner ; 
other  than  this,  I  see  no  reason  why  the  double-sharps  or 
double-flats  should  not  be  used  in  the  signature. 

When  a  key  expressed  by  double-sharps  or  double-flats 
is  required  in  a  composition,  it  is  expressed  by  means  of 
accidentals;  and  some  composers,  after  writing  a  few 
measures  with  the  accidentals  required,  make  an  enhar- 
monic change  into  the  simpler  form.  For  example,  if  the 
required  key  is  that  of  Dt,  which  will  contain  two  double- 
sharps,  the  composer  will  probably  (after  modulating  to 
that  key)  write  two  or  three  measures  in  that  key  of  D$, 
using  the  proper  accidentals;  after  which  he  will  draw  a 


6  Graded    Lessons    i)i    Ilarmoiti/ 

double  bar  and  write  the  signature  of  JLb,  which  is  the 
simpler  form,  and  continue  in  the  key  of  Eb.  By  first 
writing  a  few  measures  in  the  key  of  Dtf  he  recognizes  the 
true  relationships  of  the  keys,  and  having  done  this,  he 
continues  in  the  notation  which  is  easier  for  the  performer. 

10.  HOW  TO  WRITE  THE  SCALES. 

The  scale  should  show :  first,  the  skeleton,  that  is,  the 
figures;  second,  the  half-steps,  by  the  curved  line  between 
3  and  4,  and  7  and  8  (also  by  the  curved  line  between  the 
notes  indicated  by  these  figures)  ;  third,  the  tetrachords, 
by  means  of  the  larger  curved  line  as  shown  below; 
fourth,  the  logical  growth  of  the  signature,  by  writing  it 
after  the  scale  instead  of  at  the  beginning  of  the  line; 
fifth,  the  relationship  between  the  successive  scales,  by  a 
line  drawn  from  the  fifth  down  to  the  Tonic  of  the  next 
scale. 

To  show  all  these  points,  but  one  scale  should  be  writ- 
ten on  a  line.  You  will  find  this  much  better  for  refer- 
ence, and  it  will  be  of  great  help  to  you  in  teaching  the 
scales. 

Fig.  1. 


Ear-Training. 

11.  (Read  carefully  H.  S.,  §§47-52.)  This  work  is  a  mat- 
ter of  Groii'th — not  of  rote  learning,  li  you  are  deficient 
in  musical  hearing,  or  have  never  given  attention  to  the 
subject,  it  will  open  a  new  world  of  pleasure,  and  will 
become  a  new  avenue  of  acquisition  as  well. 

First  establish  the  feeling  for  tonality  or  tone  relations, 
through  the  ability  to  sing  (and  recognize)  the  tones  of 
the  scale  and  chord.  These  two  elements — the  scale  and 
the  chord — are  the  foundation  of  all  music.  They  are 
given  in  the  lines  a)  and  b)  of  the  Ear-training  Exercises. 

Next,  take  up  a  few  of  the  simpler  exercises — not  more 
than  six — and  work  them  every  day  for  several  weeks 
before  expecting  them  to  be  well  done.     Do  not  hurry : 


(imdcd    Lessons    in    llarmonji  7 

you  will  gain  most  by  sticking  to  the  scale  and  chord  for 
a  long  time— several  months  at  least,  in  many  cases. 
Above  all,  do  not  be  discouraged  if  you  do  not  succeed  at 
the  first  attempt. 

Especially,  listen  intelligently,  not  only  to  music  that 
is  performed,  but  also  to  every  tone  you  play  or  sing,  and 
with  this  listening  will  presently  come  a  new  perception  of 
music. 

This  work  is  to  be  done  zvithont  the  aid  of  an  instru- 
ment. Take  o;/v  convenient  tone  for  "Doh."  (For  the 
first  few  days  it  "is  allowable  to  test  the  voice,  by  touching 
the  piano  after  the  tone  or  interval  has  been  sung,  and 
while  still  sounding.) 

After  the  first  six  exercises,  and  when  the  scale  and 
chord  have  been  fairly  accurate  (though  not  necessarily  in 
their  "absolute  pitch"*)  and  are  easily  executed,  it  is  time 
to  commence  to  add  the  other  exercises  gradually,  one, 
two  or  more  each  week,  as  the  case  may  require.  But 
do  not  drop  the  scale  and  chord  or  the  simpler  exercises 
until  the  feeling  of  the  tonal  relationships  is  established, 
no:  before  you  can  both  sing  and  recognize  them  when 
given  by  another  person. 
Do  Not  Hurry  This  Work.     Give  it  Time  to  "Grozv." 

EXERCISES. 

a)  Doh  Ray  Me  Fah  Soh  Lah  Te  Doh^.  DohI  Te 

Lah  Soh  Fah  Me  Ray  Doh. 

b)  Doh  Me  Soh  Doh^  Soh  Me  Don. 


Take  breath  at  all  commas. 

(1)  Don  Me  Soh.  Doh  Me  Soh  Me  Doh  Me  Soh  Doh^ 

(2)  Doh  Doh^  Doh  Me  Soh  Doh^  Soh  Me  Doh. 

(3)  Doh  Ray  ATe,  Doh  Me,  Doh  Me  Ray  Doh,  Me 

Don. 


*  To  help  you  to  get  Absolute  Pitch,  when  you  enter  a  room  where  there  is 
a  piano,  try  to  sing  Middle  ('  or  some  other  convenient  tone.  Then  strike  it 
upon  the  piano  for  comparison  and  correction.  You  will  be  pleased  to  see  how 
after  a  short  time  you  will  be  able  to  sing  very  close  to  the  right  pitch.  The 
drill  can  be  continued  by  using  other  tones  as  well  as  C.  This  makes  one  criti- 
cal and  thoughtful  along  these  lines. 


Graded   Lessons    in    Harmon  1/ 


The 
Scale 


m' 
DOH^ 

TE 

ta  le 

LAH 

la  se 


fe 


SOH 

ba 
FAH 

ME 

ma  re 

RAY 

I  de 

DOH 

t. 
li 
s, 


(4)  DoH  Ray  Me  Fah,  Doh  Fah,  Doh 

Fah  RIe  Ray  Doh. 

(5)  Doh  Me  Soh.  Doh  Son,  Don  Son 

Fah  Me  Ray  Doh. 

(6)  Doh  Me  Soh  Lah,  Doh  Lah,  Doh 

Lah,  Te  Doh\ 

(7)  Doh  Lah. 

(8)  DoHi  Lah. 

(9)  DoH  Fah,  Doh  Lah,  Doh  Fah  Lah 

DoH^  Lah  Fah  Doh. 

(10)  Doh   Ray   Me   Fah   Son    Lah   Te. 

Doh  Te,  Doh  Te  Doh^  Te  Doh^ 
Doh. 

(11)  Doh  DoHi  Te  DohS  Doh  Te  Doh^ 

Te  Doh\  Doh  Te  Doh^  Soh  Me 
Doh. 

(12)  Doh  Me  Fah,  Doh  Me  Fah,  Doh 

Me  Doh  Fah  Doh  Me  Doh  Fah. 

(13)  Doh  Me  Soh  Doh^  Soh  Me  Doh 

Fah  Lah  Doh^  Lah  Fah  Doh. 
(Repeat.) 

(14)  Doh  Ray  Doh  Me  Doh  Fah  Doh 

Soh  Doh  Lah  Doh  Te  Doh 
Dohi. 

(15)  Doh^  Te  DoHi  Lah  Doh^  Soh 

DoH^  Fah  Doh^  Me  Doh^  Ray 
Dohi  Doh. 

(16)  Doh  Te,  Doh  Ray  Me  Doh  Te, 

Ray  Doh  Me  Soh  Te,  Doh. 

(17)  Doh   Soh  Me  Doh^  Soh   Doh  Me 

Soh  Doh^  Me  Ray  Doh. 

(18)  DoH^    Te    Lah,    Doh^    Lah    Doh^ 

Lah    Soh    Fah    Soh    Lah    Fah 
Ray  Soh  Don. 

Take  a  lower  pitch  if  necessary. 

(19)  Doni   Ray^    Me^    Ray^    Doh^    Soh 

DoHi  MeI  RayI  DohI  Sohi  Fajji 
Mei  Ray^  Doh^ 

(20)  DoH^    Me^    Ray^    Fahi    Me^    Soh^ 

FahI  Rayi  Te  Rayi  Doh^. 

(21)  Doni  Son  Lah  Te  Doh^  Soh  Me^ 

DoHi  SoH^  Soh  Doh^ 


a  railed    J.essons    in    Ilarmonii  9 

COLLATERAL    READING    AND    SUGGES- 
TIVE  NOTES.* 

12.  (1)  The  key  to  unlock  the  secrets  of  Nature,  as  mani- 
fested in  any  art  or  science,  is  the  study  of  relationships. 
Mathematics  is  the  science  of  the  relationship  of  numbers; 
astronomy,  that  of  the  relations  of  different  heavenly 
bodies.  Harmony  should  then  be,  though  it  has  not  been 
so  to  any  marked'  degree,  the  science  of  tO)ie  relationship. 
It  is  my  purpose  to  take  the  simpler  manifestations  of  Na- 
ture for  examination  in  this  regard,  and  to  draw  such  de- 
ductions from  them  as  will  be  helpful  in  later  study.  It  is 
presumed  that  the  construction  of  the  Major  scale  is 
familiar;  but  the  study  of  the  scale  in  respect  to  relation- 
ships will  reveal  principles  which  reach  to  the  uttermost 
bounds  of  the  structure  and  form  of  music. 

SCALE  CONSTRUCTION. 

(2)  Statement.  The  scale  of  Nature  and  of  Science  is 
the  Major  scale,  the  Minor  scale  being  considered  an  arti- 
ficial, derivative  scale,  since  it  is  formed  from  the  Major 
scale.  The  Major  scale  will  therefore  form  the  basis  of 
the  present  investigation. 

(3)  Statement.  A  Major  scale  is  formed  by  a  succes- 
sion of  eight  tones  (technically,  by  a  succession  of  sec- 
onds). Between  the  third  and  fourth  degrees  and  be- 
tween the  seventh  and  eighth  degrees  are  half-steps ;  be- 
tween all  other  degrees  are  whole-steps.  For  illustration, 
play  the  scale  of  C  Major. 

(4)  Statement.  This  is  the  rule  for  the  formation  of 
any  Major  scale.  Briefly  expressed  for  memorizing  it  is: 
"Between  3  and  -i,  and  between  7  and  8  are  half-steps;  all 
others  are  whole-steps." 

(5)  Deduction.  Since  the  steps  and  half-steps  fall  at 
the  (correspondingly)  same  places,  all  Major  scales  must 
be  alike.  More  scientifically  expressed,  there  is  but  one 
Major  scale,  which  appears  in  different  notations  for  con- 
venience. 


*  For  further  notes,  drills,  exercises,  topics  for  discussion,  ear-training, 
questions  and  answers,  the  student  is  referred  to  A  Key  to  Harmony  Simplified 
andaClassroom  Manual,  by  F-  H.  Shepard.  This  hook  will  be  referred  to  as 
the  Key  hereafter. 


10  Graded   Lessons    in    IIann<))i if 

(Ti)  Deduction.  Since  the  different  scales  or  keys  are 
merely  duplicates  of  a  single  type  or  scale  form,  all  chords 
and  chord  relations  appearing  in  one  key  may  be  dupli- 
cated with  similar  effect  in  any  other  key.  In  other 
words,  as  the  scales  are  alike,  so  the  chords  and  their  rela- 
tionships in  all  Major  keys  must  be  alike.  This  fact  is  of 
much  value  in  the  study  of  harmony,  since  in  effect,  we 
need  only  to  learn  the  structure  and  use  of  the  chords  of 
one  key  in  order  to  know  the  principles  obtaining  in  all 
keys.  The  foundation  principles  of  harmony  are  few  and 
simple.  The  great  need  is  to  recognize  and  apply  them  in 
a  practical  manner. 


Graded    Lcssunn    in    Harmon  1/  11 


LESSON  2. 

]\roTTO — Facility  is  as  necessary  as  kuo-a'Icdgc. 

SCALES   (Cont.) 
The  Major  Scale  (Cont.) 

13.  SCALE  DEGREES  AND  SPECIFIC  NAMES. 

Study  HS.,  §§33,  34  together.  Try  to  find  out  why 
this  sul)ject  is  important. 

14.  DRILL. 

(As  per  the  exercises  in  H.  S..  §§33,  34.) 
Taking  two  or  three  keys  each  day,  drill  thoroughly, 
both  at  the  keyboard — touching  the  proper  key  as  its  num- 
ber or  specific  name  is  mentioned — and  by  recitation  away 
from  the  keyboard. 

Continue  this  exercise  till  facility  is  gained  in  all  Major 
keys.  Probably  several  weeks'  daily  drill  will  be  neces- 
sary. 

15.  IMPORTANT  NOTE. 

Although  familiar  with  the  scales  in  the  way  of  per- 
forming them  with  speed  and  accuracy,  but  fczv  knoz^' 
the  scales  in  the  manner  here  required,  which  is  most 
important,  as  it  leads  to  the  understanding  of  many  impor- 
tant matters.  It  is  really  the  basis  of  speed  in  selecting 
chords,  in  harmonizing  a  melody  or  in  improvising.  Here 
especially,  we  must  have  not  only  knowledge  but  facility. 

Following  the  idea  expressed  in  //.  S..  §§33,  34,  take 
each  scale  in  turn  and  play  successively  the  notes  forming 
the  Tonic,  then  the  Sub-dominant  and  then  the  Dominant. 
It  is  a  good  plan  to  let  the  fingers  rest  upon  three  keys 
(the  Tonic,  Sub-dominant  and  Dominant  notes)  together 
— not  necessarily  sounding  them — that  the  mind  may  take 
them  in  as  a  group,  representing  the  most  prominent  fea- 
tures of  each  key. 

Be  prepared  to  give  this  exercise  daily  drill  for  several 
weeks. 


12  Graded   Lessons    in    llarmouij 

16.  EAK-TRAIXING. 

You  are  supposed  to  know  the  syllable  names  of  the 
tones— Doh,  Ray,  Me,  Fah,  Soh,  Lah,  Te  (or  Se),  Doh. 
It  will  help  you  in  listening,  to  associate  the  following  de- 
scriptive names  with  the  scale*  tones. 

Doh  is  called  the  Firm  Tone. 

Ray  is  called  the  Rising  Tone.    (To  illustrate,  play  Doh. 

Ray,  then  pause.) 
Me  is  called  the  Calm  Tone.     ( Plav  Doh,  Rav  Me ;  or 

Soh,  Fah  Me.) 
Fah   is  called  the   Drooping   Tone.     (Play   Rav,   Me, 

Fah;  or  Me,  Fah.  Me.) 
Soh  is  called  the  Bright  Tone.      (Play  Doh,  Soh,  Doh, 

Soh;  or  any  of  the  military  and  cavalry  calls.) 
Lah  is  called  the  Sad  Tone.     (Play   [high]    Doh,  Te, 

Lah ;  or  remember  how  the  Minor  scale  is  formed, 

starting  upon  the  sixth  step — or  Lah — of  the  Major 

scale.) 
Te  is  called  the  Leading,  or  Rising,  or  Piercing  Tone. 

(Play   up   the    scale    to    Te    and   pause,    when    the 

urgent  demand  will  be  felt  to  go  on  to  the  eighth 

step.) 

17.  EXERCISE. 

Play  or  sing  the  scale  slowly,  and  try  to  hear  and  feel 
these  qualities  in  the  different  tones. 

Note.  The  great  importance  of  this  principle  will  be 
apparent  in  the  selection  of  the  proper  scale  tones  to  express 
any  given  sentiment  or  mood.  For  example,  it  would  not 
be  right  to  emphasize  the  sixth  step,  or  Lah,  in  a  bright  or 
martial    composition.     Tins  comes  close  to  the   heart 

OF   MUSIC. 

The  appreciation  of  the  above  will  help  you  to  sing  cor- 
rectly the  Ear-training  Exercises  in  5^11.  Carry  this  point 
into  your  future  practice. 


*If  you  are  associating  the  Ear-training  with  the  key  of  C  exclusively  and 
thinking  letter  names  chiefly,  you  will  make  a  serious  mistake.  Be  careful  to 
use  the  syllable  names  and  to  "think"  by  syllables  and  by  figures  (1-3,  1-6, 
etc.)  in  connection  with  the  thought  of  the  letter  names.  Remember  that 
letter  names  (C,  G,  etc.)  express  no  relationships  whatever,  although  some 
musicians  who  are  fortunate  unconsciously  feel  and  associate  relationships  with 
the  letter  names — by  ear,  as  it  were:  but  the  use  of  the  syllables  and  figures 
forces  the  recognition  of  relationship  of  tones,  and  gives  constant  suggestion 
of  the  relative  position  of  each  tone  in  the  scale,  which  is  a  vitally  important 
feature. 


Graded  Lessons   in   TTarmoni/  13 

The  Minor  Scales. 

;\IOTTO — The  basis  of  all  music  is  the  scale.  When  you 
understand  all  that  is  involved  in  scale  relationships, 
you  will  have  a  solid  foundation  for  your  theoretical 
studies. 

18.  STUDY. 

Read  and  study  //.  .S'.,  §§35-1l>,  4(3;  also  Key,  35-42,  46. 

WRITTEN  EXERCISES. 

(a)  Write  the  exercises  in  H.  S.,  §38. 

(b)  Write  the  Melodic  Minor  scales,  following  the 
order  shown  in  H.  S.,  §38.  (For  illustration,  see  H.  S., 
Fig.  16.) 

(c)  Write  thq  scale  of  G  Major.  Then  change  it  to 
the  Harmonic  Minor  form,  by  altering  the  proper  notes 
l)y  accidentals.  (N.B.  To  save  writing  the  scale  twice, 
you  may  enclose  these  accidentals  in  parentheses.) 

(d)  Repeat   (c)  with  four  other  scales. 

(e)  Write  the  scale  of  A  Major.  Then  change  it  to 
the  Melodic  Minor   form,  by  using  accidentals  as  above. 

(f)  Repeat   (e)   with  four  other  scales. 

KEYBOARD  EXERCISES. 

(a)  Remembering  the  rule  for  placing  the  steps  and 
half-steps,  form  all  the  Harmonic  Minor  scales,  following 
the  order  of  signatures;  i.e.,  A  Minor,  E  Minor,  R  Minor, 
etc. 

(b)  Form  the  same  scales  in  the  Melodic  Minor  form. 
Play  the  above  once  each  day  for  one  week. 

Relative  Minor  and  Relative  Major. 

19.  WRITTEN  EXERCISES. 

Write  as  required  in  //.  S.,  §§3lt.  40. 

RFCITATTOX. 

Recite  (to  voursflf  <ir  to  a  friend)  the  above  exercises. 


14  Graded  Lessons   in    Harmon  1/ 

Signatures  in  the  Minor. 

20.  STUDY  H.  S.,  §§41  and  46. 

WRITTEN  EXERCISES. 

(a)  Write  the  exercises  in  H.  S.,  §41. 

(b)  Write  the  exercises  in  H.  S.,  §42. 

21.  To  Distinguish  Major  and  Minor  in  Printed  Music. 

Any  given  signature  may  indicate  either  a  IMajor  key 
or  its  Relative  Minor  key.  To  discover  which  is  intended, 
look  for  the  note  which  would  be  the  fifth  degree  (Domi- 
nant) of  the  Major  key.  If  this  note  is  raised  by  an 
accidental,  the  key  is  the  Minor.  If  unchanged,  it  is 
Major.  The  reason  for  this  is  that  it  is  this  note  which 
is  raised  to  make  the  leading  tone  in  the  ]\linor  scale. 

EXERCISES. 

Examine  Sonatas  and  other  classical  music,  for  exam- 
ples of  Minor  keys. 

22.  EAR-TRAIXIXG. 

(a)  Playing  slowly  and  thoughtfully,  contrast  Major, 
Harmonic  Minor  and  Melodic  Minor  forms  of  the  same 
scale.  Note  the  "color"  or  general  tonal  effect  of  each 
form. 

(b)  Observe  the  effect  of  melodies  written  in  the 
Minor  mode,  and  contrast  them  with  IMajor  melodies. 

(c)  Try  to  distinguish  whether  the  compositions  you 
may  hear  are  in  the  Major  or  Minor  mode.  Listen  care- 
fully. 

23.  QUESTIONS. 

(1)  How  is  the  Relative  Minor  formed? 

(2)  Where  are  the  half-steps  in  the  Harmonic  Minor 
scale? 

(3)  What  is  the  difference  lictween  the  Harmonic  and 
the  Melodic  Minor  ? 

(4)  Name  the  keys  related  to  C  Major  and  give 
reason  ihercfore. 


Graded   Lcssoii.s    in    Harmoni/  15 

(5)  How  would  yuu  discover  ;i  key  from  the  signature 
in  sharps  or  flats? 

(G)   What  is  the  signature  of  any  Minor  key? 

(7)  What  is  the  office  of  the  half-step  in  scale  con- 
struction ? 

(8)  Why  is  there  an  accidental  in  every  Harmonic 
]\Iinor  scale? 

(9)  Why  does  not  this  accidental  api)ear  in  the  signa- 
ture?    (See  answer  below,  §24.) 

(10)  Was  it  there  originally? 

(11)  How  would  you  change  a  IMajor  scale  to  an  Har- 
monic Minor  scale  of  the  same  letter  name  (Tonic 
Minor)  ? 

(12)  How  would  you  change  an  Harmonic  scale  to 
the  Major  scale  of  the  same  name? 

(13)  Name  the  Dominant  and  Sub-duminanl  in  all 
Major  and  Minor  keys. 

(1-4)  What  do  you  understand  l)y  the  term  "  Tonality"  ? 
How  is  it  developed  and  how  does  it  differ  from  the  term 
"Key"?  (Read  Key,  (10)  p.  12,  after  forming  your 
answer  to  this  question.) 

24.  ANSWER  TO  QUESTION  9. 

The  accidental  change  to  make  a  leading  tone  in  the 
Minor  scale  is  not  shown  in  the  signature  because : 

(a)  It  is  not  inherited  from  scale  to  scale;  for  exam- 
ple, Gtf,  leading  tone  in  the  scale  of  A  Minor,  becomes  0=1 
— the  shar])  is  not  inherited — in  the  next  scale,  that  of  E 
IMinor. 

(b)  Careful  examination  of  this  and  other  points 
(such  as  the  IMelodic  and  Harmonic  tendencies,  and  the 
fact  that  the  Minor  scales  appear  in  several  different 
forms,)  indicates  clearly  to  my  mind  that  the  Minor  scale 
is  not  a  true,  nature  scale,  but  is  an  artificial  or  man-made 
scale.  Further,  that  from  the  Minor  scale  we  find  no 
such  great  principles  of  relationship  as  can  be  deduced 
from  the  study  of  the  Major  scale. 

So,  in  considering  signatures,  instead  of  letting  each 
IMinor  scale  inherit  the  sharps  of  the  preceding  scale,  we 
carry  along  constantly  the  fact  that  the  Minor  scale  is 
chiefly  a  re-arrongcmcnt  of  the  resting  points  oi  the  Major 


16  Graded  Lessons   in   Ilarmonj/ 

scale  (that  is,  beginning  and  ending  upon  six  of  the  scale 
instead  of  upon  one),  and  that  the  signature  should  be 
constantly  considered  as  having  been  evolved  from  the 
Relative  Major.  \\t  like  to  think  that  the  ]\linor  scale  has 
no  real  foundation  of  its  own,  either  [Nlelodically,  Har- 
monically or  in  its  relationships,  and  therefore  its  signa- 
tures are  merely  derived  from  the  Major  scale  and  not 
inherent  in  the  Alinor  scale  itself. 

25.  THE  OFFICE  OF  THE  HALF-STEP. 

(1)  The  half-steps  by  their  location  determine  the 
quality,  or  color,  or  individuality,  of  the  scale.  For  exam- 
ple, in  the  Major  scale  they  fall  at  3 — 4  and  7 — 8,  but 
when  their  position  is  changed  to  2—3  and  5 — 6  a  certain 
kind  of  i\Iinor  scale  is  developed.  Observe  that  the  Minor 
scale  is  produced  by  changing  the  location  of  the  half- 
steps.  When  to  the  above  mentioned  Alinor  scale  another 
half-step  is  added  by  accidentally  raising  the  seventh  de- 
gree, the  Harmonic  Minor  scale  is  formed. 

Examination  of  the  old  Dorian,  Phrygian,  Lydian  and 
other  ancient  modes  (so  called)  w'ill  show  how  the 
difference  between  these  modes  resulted  entirely  from  the 
differing  locations  of  the  half-step  in  the  scale.  (N.B. 
To  represent  the  Dorian  Mode  upon  the  piano,  play  upon 
the  white  keys  exclusively  from  D  to  the  D  one  octave 
above.  The  Phrygian  is  represented  by  playing  upon  the 
white  keys,  from  E  to  the  E  above,  etc.  Observe  how 
the  Dorian  has  the  half-step  at  2 — 3  and  6 — 7,  while  in 
the  Phrygian  they  are  at  1 — 2  and  5 — 6.) 

Xow,  if  you  will  consider  the  Special  Note  on  "Indi- 
viduality of  the  Scale  Degree  and  Principle  of  Melodic 
Tendencies,''  §26,  you  will  see  how  the  character  of  any 
scale  tone  must  depend  upon  its  relative  distance  from  its 
neighboring  tones  above  and  below,  and  therefore  how 
the  half-step  has  great  power  in  giving  quality  to  the 
scale. 

The  point  is  further  illustrated  by  the  upward  ten- 
dency of  the  Leading  Tone  of  the  scale  (see  H.  S..  §152), 
and  by  the  change  in  the  effect  of  individual  scale  tones 
when  they  are  accidentally  raised  or  lowered  to  effect  a 
modulation.  (This  may  be  frequently  observed  in  the 
raising  of  the  fourth  degree  to  modulate  to  the  key  of 
the  Duminanl.  and  in  the  lowering  of  the  seventh  degree 


Graded   Lessons    in    Ilurmoni/  17 

to  modulate  to  the  key  of  the  Sub-domiiiunl.  Ihese 
changes  are  often  found  in  hymn  tunes,  to  winch  the 
student  is  referred.)  ■     •   ,      .- 

The  Chromatic  scale  also  illustrates  the  prmciple,  tor 
l,v  the  absence  of  variety  or  contrast  in  the  distances  be- 
tween the  scale  tones,  no  single  tone  differs  m  power  or 
quality  from  the  others,  and  therefore  the  scale  seems  to 
have  'no  special  place  of  beginning  or  of  endnig  unless 
such  place  is  indicated  by  the  rhythm  or  accompanymg 
chords.  (See  below  Special  Note  on  the  Scale  1  en- 
dencies.) 

(2)   The   coincidence   of   the   melodic   tendencies   and 
the  locations  of  the  half-steps  in  the  scale  has  an  impor- 
tant  bearing   upon   the   "Office   of   the    Half-step,     when 
considered  in  connection  with  the  thought  that  the  quality 
of  each  scale  tone  depends  upon  its  relative  nearness  to 
its  neighbors,  and  that  by  changing  this  relative  nearness 
— bv  changing  the  places  of  the  half-steps  in  the  scale— 
we 'can  change  the  quality  of  any  given  scale  tone  and  so 
change  the  quality  of  the  whole  scale,     tor  example,  by 
lowering  the  third  degree  of  a  Major  scale  the  upward 
form  of  the   Melodic   Minor  scale  is  formed.     Or  it  the 
fourth  degree  of  a  Major  scale  is  raised  a  half-step,  a 
completely  new  scale,  that  of  the  Dominant,   is  formed. 
(3)    Another  rich  suggestion  may  be  found  in  the  fact 
that  whole   chords   may  be  changed,   as    from   Major   to 
Minor,   etc.,    by   changing   a   single   note   by   a   half-step. 
For  example,  C-E-G  is  the  triad  of  C  Major,  while  C-Eb-( , 
is  the  triad  of  C  Minor.  , 

The  above  thoughts   illustrate  some  of  the  powers  o 
the    half-step.     The    subject,    though    possibly    somewhat 
indefinite  at  first,  will  grow  upon  the  mind  as  advancement 
!s  made  in  the  study.     Occasional  review  should  be  made 
of  this  and  other  foundation  principles. 

96    INDIVIDUALITY  OF  SCALE  DEGRIiES.  PRIN- 
CIPLE OF  MELODIC  TENDENCIES. 

See  also  H.  .9.,  §152  r/  .?r^7. 

See  also  Collateral  Reading.  Lesson  4.  ^.>0,  (!.,)-( 14) 

The  effect  of  a  scale  is  found  by  considering  several 

tones  in  .succession,  or  in  relation   to  each  otlu^.  not  by 

thinking  of  tones  isolated  one  from  the  other.     Each  tone 

of  the  scale  may  therefore  be  considered  as  lying  between 


18  (iradcd   Lessons    in    Ilarmoni/ 

two  other  tones,  that  is,  between  the  tone  next  above  and 
the  one  next  below  (e.g.,  in  the  scale  of  C,  the  note  D 
lies  between  C  and  E).  Now  if  a  tone  is  nearer  to  its 
neighbor  on  one  side  than  on  the  other,  it  is  found  to  have 
a  tendency  to  progress  to  that  nearer  neighbor  rather  than 
to  the  other,  and  this  is  called  melodic  tendency.  To 
illustrate,  in  the  scale  of  C  Major,  E  is  nearer  to  F  than 
to  D,  therefore  it  tends  toward  F  rather  than  toward  D. 
If,  however,  the  neighboring  tones  are  equally  distant 
the  tone  is  free  to  progress  in  either  direction.  For  exam- 
ple, in  the  same  scale  A  is  equally  distant  from  G  on  the 
one  side  and  from  B  on  the  other.  A  is  therefore  a  free 
ncntral  and  not  a  tendency  note. 

It  should  be  observed  that  the  above  theory,  while 
differing  in  substance  from  that  given  in  H.  S.,  reaches 
the  same  result,  viz.,  that  the  tendency  )iotcs  of  the  scale 
are  found  zvhere  the  half-steps  occnr. 

A  slightly  different  theory  is  advanced  by  Goetschius, 
as  follows:  The  Tonic  chord  (for  example  C-E-G-C  in 
the  key  of  C)  represents  the  chief  points  of  rest  in 
the  scale  and  key.  These  notes  may  also  be  called  "in- 
active" notes,  and  the  other  tones  of  the  scale,  because 
each  tends  toward  one  of  these  points  of  rest,  are  called 
"active"  or  tendency  tones.  The  active  tones  tend  always 
toward  the  nearest  point  of  rest.  In  results  this  theory 
corresponds  with  the  other  except  in  the  case  of  the  sixth 
degree  of  the  scale,  which  is  classed  as  an  "active"  tone, 
as  it  is  nearer  to  the  fifth  degree  of  the  scale  than  to  the 
eighth.  The  theory  advanced  by  Goetschius  applies  par- 
ticularly to  the  treatment  of  melodies  while  the  other 
applies  directly  to  harmonic  progressions. 

By  carefully  comparing  these  three  slightly  differing 
theories,  we  trust  you  will  gain  a  real  insight  into  this 
matter,  which  is  one  of  the  most  important  underlying 
principles  of  musical  theory,  explaining  in  thousands  of 
cases  the  reasons  of  ineffective  and  unmusical  progres- 
sions. 

Speciai.  XiiTK  I.*  About  Tendency  Tones.  Active  Tones 
and  Resting  Tones.  If  we  think  of  the  two  tetrachords  in  the 
scale,  it  is  easy  to  conceive  of  the  third  degree  as  a  Leading 
Tone  to  4  just  as  7  is  the  Leading  Tone  to  8.  This  upward 
tendency  of  the  third  degree  appears  when  wo  modulate  to 
the   key  of  the   Sub-dominant. 


*  From  lessons  to  ijupils,  1913. 


Graded   Lessons    in    Harmon  1/  19 

But:  the  restful  quality  of  the  Resting  Tones  (1.  3,  5, 
and  8)  is  most  important,  and  more  constantly  in  evidence; 
and  the  activity  of  3  is  not  evident  unless  we  modulate  or 
manage  the  progressions  rhythmically  so  as  to  come  to  a  stop 
on  the  Sub-dominant  chord.  Therefore  I  do  not  empha- 
size the  upward  tendency  of  3,  although  it  is  scientifically 
correct,  perhaps.  I  now  think  it  more  practical  to  call  3  a 
Resting  Tone  and  ignore  the  tendency ;  so  please  forget,  until 
later,  that  3  tends  up  to  the  fourth. 

This  point  is  about  the  only  thing  in  Harmony  Simpli- 
fied that  I  would  like  to  change. 

Special  Note  II.*  About  the  Tendency  of  the  Third 
Degree  of  the  Scale.  When  we  consider  the  tetracliords  sep- 
arately, we  see  that  the  third  degree  is  to  the  fourth  degree 
(constructively)  just  what  the  seventh  degree  is  to  the  eigiitli 
degree.  Consequently  it  is  not  difficult  to  recognize  in  the  third 
degree  a  sort  of  leading  tone  to  the  fourth  degree.  In  fact  this 
becomes  apparent  as  soon  as  we  modulate  to  the  key  of  the 
Sub-dominant :  hence  the  statement  of  the  upward  tendency 
on  the  part  of  the  third  degree.  This  I  was  taught  by  Eugene 
Thayer,  a  great  philosopher  as  well  as  musician.  But  at  that 
time  1  knew  nothing  of  the  Resting  and  Active  Tones  of 
the  scale,  and  all  that  they  mean  in  music.  I  now  prefer 
to  frankly  abandon  the  thought  of  a  tendency  on  the  part 
of  the  third  degree,  since  to  make  it  effective  we  have  to 
depart  from  the  key,  to  a  certain  extent  at  least.  The  classi- 
fication and  consideration  of  a  tendency  of  the  third  degree  are 
unnecessary  to  the  understanding  of  the  fundamental  dis- 
sonant chords  (Dom.  Sevenths,  Dim.  Sevenths,  Aug.  Sixths, 
etc.)  ;  and  there  is  so  much  to  be  gained  by  taking  the  third  as 
a  resting  point  in  tlie  scale  as  explained  in  the  Key  to  Har- 
mony Simplified,  page  8,  §48,  that  we  will  simply  ignore  this 
tendency  as  a  far-fetched  and  disturbing  element  which  we 
will  eliminate  from  our  work,  for  the  present. 

(This  point  is  about  the  only  thing  in  Harmony  Sim- 
plified that  I  would  like  to  change.) 

Special  Note  III.  We  get  perhaps  most  of  the  ten- 
dency feeling  unconsciously  through  long  association  with 
chords.  For  example,  nine  out  of  ten  pupils  have  never  felt 
or  thought  of  tendencies — or  at  least  have  not  mentally  rec- 
ognized tliem.  So  in  tlie  Minor  we  have  less  feeling  for  ten- 
dency between  II  and  III,  or  V  and  VI,  since  the  chords  do 
not  emphasize  the  feeling :  I  would  recognize  only  very 
slight  melodic  tendencies  in  tlie  .Minor  at  these  points.  In 
fact,  the  absence  of  law  in  the  Minor  (as  compared  with 
the  Major)  is  evidence  to  me  that  it  is  only  an  arbitrary, 
man-made  form,  contrasting  with  the  divine  law  in  the  Major. 

*  l'"rom  lessons  to  pupils,  1913. 


20  Graded   Lessons   in   Ilannonii 

27.  NOTE  ABOUT  THE  SIGNATURE  OF  Db  MINOR. 
As  this   scale   is  the  Relative  Minor  of   Fb   Major  it 

would,  logically,  have  the  same  signature,  which  is  eight 
flats,  and  would  therefore  include  one.  double-flat ;  but  in 
practice  it  is  never  used,  or  at  least  I  have  never  seen  it : 
the  enharmonic  key  (CS  Minor)  is  used  instead.  If, 
however,  the  laws  of  form  require  the  key  of  Db  Minor 
instead  of  C*  Minor,  it  would  be  expressed  by  accidentals, 
so  far  as  I  know.  Yet,  if  someone  were  bold  enough  to 
publish  a  piece  in  the  key  of  Db  Minor  and  include  the 
necessary  double-flat  in  the  signature,  I  would  commend 
it ;  for  I  see  no  reason  why  double-flats  or  double-sharps 
should  not  be  used  in  the  signature  with  perfect  propriety. 
In  your  written  exercises  you  may,  if  you  wish,  write  the 
signature  of  Db  Minor  with  the  double-flat,  although,  as 
I  say,  custom  does  not  support  us  in  this. 

COLLATERAL  READING. 

28.  INDIVIDUALITY  OF   SCALE  TONES;   INTER- 

NAL RELATIONS. 

(1)  Statement.  The  Tonic  or  Key  Center.  When  any 
note  is  chosen  as  the  Tonic,  or  starting  point  of  a  scale, 
a  key-center  is  established,  and  certain  definite  relation- 
ships are  developed  between  the  different  scale  tones, 
which  are  expressed  by  the  terms  Dominant,  Leading 
Tone,  Sub-dominant,  etc.  These  relationships  are  in- 
herent in  the  scale,  and  are  of  importance  in  our  study. 

(2)  Statement.  Resulting  from  the  relations  just 
mentioned,  certain  tones  of  the  scale  possess  peculiar 
qualities  which  may  be  called  tendencies.  Investigation 
proves  that  there  are  marked  tendencies  on  the  part  of  the 
tone  on  the  seventh  degree  to  ascend,  and  of  the  tone 
on  the  fourth  degree  to  descend,  when  used  under  certain 
conditions  in  melodic  passages.  Another  tendency,  less 
marked,  is  that  of  the  third  degree  to  ascend.*  These  are 
called  melodic  tendencies,  since  they  exist  independently 
of  harmonic  effects.  They  are  not  laws,  and  these  tones 
are  not  obliged  always  to  follow  the  directions  indicated; 
they  are  simply  tendencies,  or  influences,  which  point 
Nature's  way,  and  which,  under  the  right  conditi(Mis,  may 
become  sufficiently  powerful  to  control. 

*Read  Special  Notes  1  and  II,  326. 


Graded   T.rssoiis    in    Ilarmoni/  21 

(.'5)  [JciJuctioii.  Since  these  tendencies  are  ii^lierent 
in  the  single  tone,  we  may  expect  them  to  be  effective  when 
tones  arc  combined  in  chords.  This  fact,  hitherto  but 
little  considered,  is  one  of  the  most  potent  forces  in 
Theory,  and  will  be  considered  again  after  a  short  time. 

(4)  Exercise.  Find  the  tendency  notes  in  different 
scales. 


22  Graded  Lessons   in   Harmon i/ 


LESSON   3. 

SCALES   (Cont.) 
Related  Keys. 

Motto — Many  important  relationships  and  laws  of  music 
rest  upon  the  scale  as  a  basis. 

29.  The  related  keys  of  any  Major  key  are:  first,  the 
keys  of  the  Dominant  and  Sub-dominant  Major;  then, 
the  related  INIinors  of  all  three,  (i.e.,  the  Relative  Minors 
of  the  Tonic,  Dominant,  and  Sub-dominant)  ;  and  lastly 
(added  by  some  authorities,)  the  Parallel  Minor,  or  Minor 
key  of  the  same  name.  To  illustrate,  the  keys  related  to 
C  Major  are:  first,  G  ^Major  and  F  Major  (which  are 
respectively  the  key  of  the  Dominant  and  Sub-dominant)  ; 
then,  A  Minor,  E  Minor  and  D  Minor  (which  are  respec- 
tively the  Relative  Minors  of  C,  G  and  F;  and  lastly, 
C  Minor  (which  is  the  Parallel  Minor). 

WRITTEN  EXERCISES. 

\\'rite  the  kevs  related  to  each  of  the  following  Major 
keys:  G;  D;  A;'E;  B;  F::  ;  C? ;  Db  ;  Ab  ;  Eb  ;  Bb  ;  F. 
Read  also  H.  S.,  §334. 

30.  The  related  keys  of  any  ^Minor  key  are :  first,  the 
Dominant  and  Sub-dominant  Minor;  next,  the  Relative 
Majors  of  all  three  (the  Tonic,  Dominant  and  Sub-domi- 
nant) ;  and  lastly,  the  Parallel  Ma:jor  key  (^Major  key  of 
the  same  name). 

WRITTEN  EXERCISES. 

Write  the  kevs  related  to  each  of  the  following  Minor 
keys  :  A  :  E  ;  B  :  G  ;  C  ;  F« ;  Bb  ;  Eb  ;  Ab  ;  Db. 

The  Chromatic  Scale. 
31.  STUDY  77.  .S".,  §43. 

WRITE  Chromatic  scales  in  the  following  Major 
keys,  by  first  writing  the  regular  (Diatonic)   Major  scale 


Graded   Lessons    in    Ilarmonii  '  2?> 

in   the  key,  using  the   signature,   and   then   filling   in   the 
Chromatic  notes: — In  the  key  of  1);  of  A;  of  Bb. 

Write  in  figures  a  formula  for  the  Chromatic  scale 
which  will  apply  equally  to  all  keys. 

32.  STUDY  H.  S.,  §44. 

First  read  the  synopsis  in  H.  S.,  §44.  Then,  referring 
to  the  text-book,  make  an  original  synopsis  from  the  text- 
book, trying  to  see  how  one  subject  grows  out  of  another. 

33.  INTRODUCTION  TO  CHORD  BUILDING. 

It  is  well  to  associate  the  Tonic  chord  (or  chord  upon 
the  first  degree  of  the  scale)  with  the  study  of  the  scales. 
It  should  be  played  with  one  hand  alone,  and  in  its  three 
positions  (for  example,  C-E-G ;  E-G-C;  G-C-E;  play 
these  three  forms).  This  is  described  in  H.  S.,  §90  and  in 
the  Key,  9G. 

KEYBOARD  EXERCISES. 

Play  the  Tonic  triad  in  its  three  positions  in  all  Major 
keys;  also,  if  not  too  difificult,  in  all  Minor  keys.  Com- 
mence at  a  slow  tempo  (e.g.,  M.  M.  (50,  with  two  beats  to 
each  chord)  and  increase  the  speed  only  as  the  forms 
become  familiar. 

N.B.  This  exercise  does  not  logically  belong  here,  but  it 
will  save  time  later  to  become  familiar  with  it  now. 

34.  QUESTIONS  11--20,  Key.  pp.  13-14. 

35.  ANSWERS  TO  QUESTIONS  11-20,  Key,  pp.  13-14. 

(11)  By  the  term  Related  Keys  is  understood  keys 
which  have  several  notes  in  common ;  or  better  still,  sev- 
eral chords  in  common,  since  nearly  all  scales  have  several 
notes  in  common. 

(12)  In  the  simplest  series  of  relationship  each  key 
is  a  fifth  above  or  below  its  nearest  related  key.  This 
forms  what  is  called  the  series  of  "Quint  Relationships." 
The  other  series  is  the  series  of  Relative  Minor  and  Rela- 
tive Major  Relationship  which  might  be  described  as  the 
series  of  "Tierce  (or  Third)  Relationships."  In  these 
two  relationships  we  can  again  see  something  of  the  logic 


24  Graded  Lessons    in   llcirmoni/ 

of  chord  structure,  as  the  above  relationships  are  illus- 
trated in  simple  triads. 

(13)  The  word  Chromatic  might  be  explained  in  two 
almost  opposite  ways.  First  explanation :  The  term 
means  color;  and  the  Chromatic  tone  instead  of  being 
an  original  entity,  possessing  relationship  of  its  own  with 
other  tones  in  the  key,  is  merely  a  colored  or  altered  form 
of  some  actual  scale  tone.  Second  explanation :  The 
word  Chromatic  might  be  considered  as  a  colorless  scale 
since  the  element  of  contrast  is  absent  for  the  reason  that 
the  steps  of  the  scale  are  all  alike.  This  might  be  con- 
sidered to  make  the  scale  wanting  in  color  contrast,  which, 
like  a  roll  of  tape  can  be  cut  off  at  any  point  and  seems 
to  have  no  design  in  beginning  or  in  ending.  In  the 
Major  Diatonic  scale  the  half-steps  and  whole-steps  form 
such  contrast  that  we  are  conscious  of  the  individuality 
of  the  tones  comprising  the  scale,  which  individuality  is 
entirely  wanting  in  the  Chromatic  scale.  Read  very  care- 
fully "The  Office  of  the  Half-step,'"  Lesson  2,  §2.5,  and 
"Individuality  of  Scale  Degrees,"  Lesson  2,  §26. 

(14)  It  should  be  clearly  seen  that  the  Chromatic 
tones  are  simply  laid  upon  or  interposed  between  the 
tones  of  the  Diatonic  scale,  and  that  the  Diatonic  scale  is 
the  essence  of  the  Chromatic,  and  all  its  relationships  are 
just  as  present  as  when  the  Chromatic  tones  are  omitted, 
leaving  simply  the  Diatonic  scale.     Read  Key,  43. 

(15)  In  general,  sharps  are  used  going  upward  and 
flats  are  used  going  downward ;  but  it  should  be  remem- 
bered that  a  natural  may  sometimes  perform  the  ofifice  of 
an  accidental  sharp  or  flat,  if  it  is  used  after  a  sharp  or 
flat  normal  scale  tone. 

(IG)  When  a  letter  with  sharp  or  flat  appears  in  the 
regular  course  of  a  scale,  it  is  just  as  natural  to  that  scale 
as  any  white  key  in  the  scale  of  C,  since  all  are  scale 
tones.  In  singing,  the  throat  does  not  recognize  black 
keys — all  are  alike  natural  to  the  ear  if  in  the  scale.  A 
little  Hibernian  conundrum  illustrates  the  point ;  I  fre- 
quently give  it  in  class  work :  "When  is  a  sharp  not  a 
sharp?"  The  simple  answer  is:  "When  it  is  natural  to 
the  scale."  Though  it  may  be  rather  silly,  it  contains  a 
most  important  truth,  which  you  may  need  to  consider 
seriously  and  persistently  in  order  to  gain  the  full 
meaning. 


(traded   Lcsnoim    in    Ildinioiii/  25 

(17)  This  formula  is  really  the  same  as  the  fornmla 
for  the  Diatonic  Major  scale  given  in  Lesson  1  with  the 
addition  of  the  interposed  Chromatic  or  accidentally 
altered  notes : 

Upward:  1,  1«,  2.  2«,  3,  4,  4$,  5,  5$,  6,  6«,  7,  8. 
Downward:  8,  7,  7b,  fi,  Gb,  5,  5b,  4,  3,  3b,  2,  2b,  1. 

If  you  will  follow  this  formula  you  can  write  the  Chro- 
matic scale  correctly  in  any  Major  key.  From  this  you 
will  understand  what  changes  to  make  to  write  it  in  a 
Minor  key.  In  all  cases  remember  that  the  Diatonic  scale 
should  appear  unchanged  and  the  other  notes  represented 
as  Chromatics. 

(18)  The  chromatically  altered  tones  always  appear 
folloiving  the  unaUered  or  scale  form  of  the  same  letter, 
and  never  before  it.  For  example,  in  making  a  note  we 
would  never  use  FJ  before  F. 

(19)  Some  composers  use  the  sharp  fourth  and  flat 
seventh  (in  the  key  of  C  this  would  be  Flf  and  Bb)  in 
both  directions,  not  changing  Fff  to  Gb  coming  downward 
or  Bb  to  Aff  going  upward.  Their  reason,  I  believe,  is 
that  these  two  tones  are  characteristic  of  the  Dominant 
and  Sub-dominant  keys  respectively,  and  being  so  closely 
related  and  being  frequently  used  for  modulating  from  the 
key,  they  have  a  legitimate  place  of  their  own.  The 
writer  does  not  fully  agree  with  this  and  will  show  when 
we  study  Attendant  Chords  in  H.  S.,  how  G*  or  many 
other  accidentals  may  be  shown  to  be  just  as  close  to  the 
key  as  are  these  tzvo  favored  accidentals. 

(20)  Originally  the  word  Diatonic  meant  "through  all 
the  tones"  or  through  all  the  keys.  This  would  seem  to 
imply  the  longer  scale  consisting  of  two  tetrachords  as 
contrasted  with  the  short  or  single  tetrachord  scale.  Its 
applied  meaning  in  modern  music  is  a  scale  having  one 
tone  upon  each  letter  and  using  all  the  letters  as  in  regu- 
lar Major  or  Minor  scales.  It  is  also  especially  used  in 
contrast  with  the  Chromatic  scale,  or  scale  in  which  there 
are  two  sounds  or  two  tones  representing  one  letter. 


26  Gradt'd   Lessons    in    Ilarmoni/ 

Comparison  of  Terms  Diatonic,  Chromatic,  Enliarmonic. 

"A    DIATONIC    change    means    change    of    i-rrcii    and 

change   of  LETTEK." 

"A  CHROMATIC  change  means  change  of  pitch  but  not 
change  of  letter." 

"An  ENHARMONIC  change  means  change  of  letter  but 
not  change  of  pitch." 

3fi.  NOTE  OX  THE  CHROMATIC  NOTATION. 
This  formula  might  be  called  the  Harmonic: 

1,  2b,  2=,  3b,  3=,  4,  4$,  5,  Gb,  65,  7b,  7=,  1. 

This  recognizes  the  flat  Third  and  the  flat  Sixth  as  sug- 
gested by  the  Minor  mode  ;  the  sharp  Fourth  and  the  sharp 
Seventh  as  being  the  characteristic  accidentals  leading  to 
the  keys  of  the  Dominant  and  Sub-dominant  respectively, 
which  keys  are  included  in  the  group  of  related  keys — 
or  what  is  sometimes  called  the  Larger  Tonality.  The  flat 
Second  is  also  included  by  reason  of  its  use  in  the  chord 
of  the  Augmented  Sixth  based  upon  the  Dominant  and 
also  upon  the  Neapolitan  Sixth,  neither  of  which  can  be 
made  clear  until  you  have  studied  further. 

Frequently  this  harmonic  form  is  combined  with  or 
substituted  for  the  regular  ascending  and  descending 
forms  as  first  given  in  this  lesson.  After  becoming  ac- 
quainted with  these  various  forms  of  the  Chromatic  scale 
and  the  erratic  way  in  which  it  is  often  noted,  you  will  be 
inclined  to  think  there  is  no  positive  rule,  but  you  will  at 
least  understand  the  principles  ujion  which  different  com- 
posers proceed. 

37.  EAR-TRAINING. 

How  to  Distinguish  Half  and  Whole-steps. 

The  following  suggestions  usually  prove  helpful.  They 
are  built  upon  the  law  of  association. 

(1)  The  half-step  upward  suggests  to  the  mind  the 
ascending  Chromatic  scale. 

(2)  The  half-step  downward  suggests  the  desire  to 
immediately  return  to  the  starting  tone.  To  illustrate, 
play  8,  7,  8  of  the  scale  a  few  times  in  succession  and  then 
play  8,  7  alone,  when  the  ear  will  demand  the  completion 
of  the  group  and  the  return  to  the  Key  Note.     Singers 


(traded   Lcssou.s    in    Tldiriunii/  27 

will  recognize  this  under  the  syllahle  order  of  I)(ili',  'l\\ 
Doll'.  It  is  merely  a  completion  of  the  uiiward  tendency 
of  the  leadiiig  lone. 

(o)  The  whole-ste])  upward  will  su.t;s;est  to  the  mind 
the  continuation  of  the  Diatonic  Major  scale. 

(4)  The  whole-step  downward  will  suggest  another 
whole-step  (downward)  to  complete  cadencing  series  of 
tones  like  3,  2,  1  of  the  scale.  This  is  an  outgrowth  of 
the  consideration  of  the  Resting  and  Active  Scale  Tones 
as  described  in  the  Key,  48. 

With  the  aid  of  the  above  the  student  will  be  enabled 
to  distinguish  between  an  ascending  half  and  ascending 
whole-step,  for  the  one  will  suggest  the  Chromatic  scale, 
while  the  other  suggests  the  Diatonic  scale.  Similarly,  a 
descending  half-step  can  be  distinguished  from  the  de- 
scending whole-step,  for  the  half-step  suggests  the  imme- 
diate return,  while  the  descending  whole-step  suggests 
further  descent. 

Please  study  the  above  carefully. 


28  Graded  Lessons   in   Harmon ^ 


LESSON   4. 

SCALES   (Cont.) 

Special  Advanced  Work. 

Note.  This  lesson  is  not  obligatory  or  even  positively 
necessary.  Yet,  if  you  fully  master  it.  you  will  understand 
something  of  the  wonderful  symmetry  of  Nature  as  re- 
vealed  in    ]\Iusic. 

38.  THE  MEANING  OF   SCALE  RELATIONSHIPS. 
STUDY  H.  S.,  §§13-29.     Also  Collateral  Reading,  §39. 

EXERCISES. 

Write  out,  and  also  work  out  at  the  keyboard,  all  the 
illustrations  and  exercises  mentioned.  Try  to  prove  or 
illustrate  each  individual  statement,  and  find  its  bearing 
on  the  rest  of  the  matter.  If  you  understand  the  exposi- 
tion, try  and  make  an  original  demonstration  of  the  same 
principles,  using  (as  far  as  possible)  different  keys  to 
illustrate.  Use  your  own  language  as  much  as  possible, 
first  saturating  your  mind  with  the  ideas  by  repeated  read- 
ings of  the  text  mentioned  above.  Then  answer  the  fol- 
lowing questions. 

(1)  Do  you  see  that  7  of  one  scale  (seventh  de- 
gree of  the  scale)  is  the  same  letter  as  the  fourth  in  the 
"preceding"  scale? 

(2)  Knowing  that  only  one  tone  is  changed  in  going 
from  one  scale  to  the  next  in  order,  do  you  see  that  the 
change  is  made  by  creating  a  new  leading  tone  (by  the 
use  of  a  new  sharp)  ;  or  by  restoring  an  old  leading  tone 
(either  by  taking  away  a  sharp  or  by  adding  a  flat)  ? 

(3)  In  connection  with  question  2.  do  you  see  that 
creating  a  new  leading  tone  takes  us  to  the  key  having  one 
more  sharp  (the  next  scale  in  ascending  order),  while 
restoring  an  old  leading  tone  by  removing  a  sharp  (or 
adding  a  flat)  takes  us  to  the  next  key  in  descending 
order? 

(4)  Does  this  mean  to  you  that  taking  away  a  sharp 


Graded   Lessoim    in    llannoiiij  29 

is  equivalent  to  adding  a  flat,  or  that  taking  away  a  flat 
is  equivalent  to  adding  a  sharp? 

(5)  Do  you  recognize  that  by  going  upward  a  fifth 
you  will  reach  the  same  letter  as  by  going  downward  a 
fourth?  Can  you  see  this  in  the  arrangement  of  sharps 
and  flats  in  the  signature?  Do  you  also  see  that  going 
upward  a  fourth  is  the  same  as  going  downward  a  fifth? 

(6)  Do  you  realize  that  the  "Order  of  Sharps"  gives 
a  series  of  fifths  similar  to  the  order  of  scales,  though 
not  commencing  on  the  same  letter? 

(7)  Can  you  describe  and  illustrate  a  portion  of  the 
Circle  of  Keys— for  example,  the  changes  made  and  the 
inner  meanings  involved  in  the  keys  of  C-G-D-A? 
(N  B.)  Take  for  a  model  answer  Collateral  Reading,  (1)- 
(2),  §39. 

(8)  Similarly  describe  the  descending  process  of  that 
portion  of  the  circle  commencing  with  D  (two  sharps) 
and  taking  in  succession  the  keys  of  G-C-F-Bb.  See 
Collateral  Reading,  (6),  §39. 

(9)  Describe  the  process,  ascending,  in  the  following 
keys :  Bb,  F,  C,  G,  D. 

(10)  Can  you  give  your  impression  of  the  relations  of 
sharps  and  flats,  as  shown  in  this  process? 

SPECIAL  QUESTION. 

Do  you  know  any  practical  reason  for  studying  or 
even  for  the  existence  of  the  keys  with  double-sharps  and 
double-flats,  when  there  is  a  simpler  expression  for  the 
same  thing? 

Anszccr.  To  illustkate  the  need  of  double-sharp  keys: 
A  law  of  form  requires  the  frequent  modulation  into  the  key 
of  the  Dominant.  If,  for  example,  tlie  Tonic  is  the  key 
of  CJ,  the  Dominant  would  have  to  l)e  the  key  of  G*— not 
the  kev  of  Ab.  This  is  because  the  lifth  degree  of  the  scale 
of  CS'is  Gtf  and  not  .-Kb.  The  key  of  Gt  (a  double-sharp 
key)  is  thus  related  to  the  key  of  Ct,  wliereas  the  key  of  Ab 
is  totally  imrelated.  It  is  therefore  on  account  of  the  rela- 
tioiisliit  of  tlic  keys  that  it  is  necessary  sometimes  to  use 
a  (louble-sliarp  or  a  donblc-tiat  key  instead  of  its  simpler 
equivalent  key. 


30  Graded   Lessons   in   Ilarmoni/ 

COLLATERAL   READING. 

39.  SCALE     ASSOCIATIONS.     EXTERNAL     RELA- 
TIONS. 

(1)  Statement.  Successive  scales  are  formed  by 
using  the  note  upon  the  fifth  degree  of  each  scale  as  the 
Tonic,  or  starting  tone,  of  the  next  scale.  Following  this 
plan,  each  scale  will  have  one  more  sharp  than  the  pre- 
ceding scale. 

(2)  Exercise  and  Illustration.  Starting  with  the  note 
C,  form  successive  Major  scales  at  the  keyboard  or  in 
writing,  or  both.  The  fifth  degree  of  the  scale  of  C  is 
the  note  G,  which  will  become  the  Tonic,  or  starting  note, 
of  the  second  scale.  This  scale  of  G  will  have  one  sharp. 
The  fifth  note  of  the  scale  of  G  is  D,  which  will  become 
the  Tonic  of  the  third  scale.  The  scale  of  D  has  one 
more  sharp  than  G,  or  two  sharps.  Continue  similarly 
to  use  the  fifth  degree  of  each  scale  as  the  Tonic  of  the 
next  scale. 

(3)  Statement.  This  series  may  be  continued,  by 
using  double-sharps,  to  the  scale  of  B-sharp.  This  is 
called  the  circle  of  sharps  and  includes  every  key,  white 
or  black,  in  the  octave;  that  is,  twelve  keys,  and  so  twelve 
scales. 

(4)  Statement  and  Deduction.  In  each  scale  all  the 
sharps  of  the  previous  scale  are  retained,  and  one  new 
one  added.  This  new  sharp  is  always  placed  on  the  sev- 
enth degree,  or  leading  tone,  of  the  scale,  and  may  be 
called  the  "Characteristic  Sharp."  From  this  fact  we  are 
able  to  recognize  any  Major  scale  instantly,  by  noting  the 
fact  that  the  keynote  of  any  scale  is  one  half-step  above 
the  seventh  degree,  or  leading  tone.  The  seventh  degree 
is  revealed  by  the  location  of  the  new  sharp,  which  is 
always  placed  at  the  right  in  the  signature,  as  it  is  the 
only  one  added.  Therefore,  the  key  is  recognized  as 
being  one  half-step  above  the  right-hand  sharp  in  the 
signature.  To  illustrate:  In  the  signature  of  four  sharps, 
D-sharp  is  found  furthest  to  the  right.  The  keynote  will 
therefore  be  one  half-step  higher  than  D-sharp,  and  must 
be  in  the  key  of  IC.  Another  and  far  more  useful  appli- 
cation of  this  ])rinciplc  will  be  shown  later  in  the  discov- 
ery of  any  fundamental  foreign  chord,  one  of  the  most 
vague  and  difficult  matters  in  the  study  of  Theory. 


iiradid    Lessons    in    Harmon  if  ^\ 

(5)  Deduction.  Scales  having  most  notes  in  common 
(notes  belonging  to  both  scales)  form  what  is  called  re- 
lated keys.  The  related  keys  or  scales  are,  then,  the  one 
having  one  more  sharp  and  the  one  having  one  less  sharp, 
since  in  each  case  only  one  note  is  altered  to  create  the 
next  succeeding  scale.  For  example,  the  keys  most 
closely  related  to  the  key  of  Ci  are:  key  of  D,  since  that 
has  one  more  sharp  than  G;  and  key  of  C,  since  that  has 
one  less  sharp  than  G.  By  a  similar  reasoning— the  notes 
in  common — the  key  of  the  Relative  ]\Iinor  is  also  consid- 
ered as  a  related  key.  These  are  the  keys  most  closely 
related  to  any  given  key ;  the  one  having  one  more  sharp, 
which  is  the' key  of  the  Dominant:  the  one  having  one 
less  sharp,  the  'Sub-dominant,  and  the  Relative  INlinor. 
To  these  may  be  added,  to  complete  the  list  of  related 
kevs,  the  Relative  Minor  of  the  Dominant  and  the  Rela- 
tive Minor  of  the  Sub-dominant.  These  relationships,  the 
result  of  similarity  of  construction,  form  the  basis  of  the 
choice  of  keys  in  classical  compositions.  For  example, 
in  the  sonata  form  it  is  customary  to  place  the  second 
theme  in  the  key  of  the  Dominant.  Similarly,  in  fugue 
the  ''answer"  to'  the  subject  is  placed  in  the  Dominant. 
In  song  form  the  phrases  are  found  usually  in  one  or 
another  of  the  related  keys.  This  relationship,  when 
applied  in  composition,  secures  unity  in  variety.  It  also 
illustrates  how  simple  laws  of  Nature  affect  and  control 
the  highest  art  forms. 

(G)  Statement.  Beginning  with  the  key  of  C,  the 
circle  of  keys  with  sharps  was  constructed  by  taking  the 
fifth  degree  of  one  scale  as  the  Tonic  of  the  next  succeed- 
ing scale.  This  process  may  naturally  be  reversed,  for  if 
we  start  with  a  key  having  one  or  more  sharps  we  may 
find  the  key  which  shall  have  one  less  sharp,  by  counting 
downward  as  many  degrees  as  were  counted  upward 
before.  I-'or  exam])le,  let  us  start  with  the  scale  of  D, 
having  two  sharps — F-sharp  and  C-sharp.  (The  student 
should  follow  this  carefully  at  the  keyboard  or  in  writing.) 
To  find  the  scale  which  sliall  have  only  one  sharp,  simply 
follow  the  scale  of  D  downward  to  the  fifth  note  from  the 
top,  thus:  1).  CS,  B,  A,  G.  The  fifth  note  touched  is  G. 
which  will  be  the  Tonic  of  the  scale  having  only  one 
sharp.  C()mi)aring  the  scales  of  D  and  G.  we  find  that 
since  C-sharp  is  the  leading  tone  of  the  scale  of  D,  and 
therefore  the  one  to  receive  the  new  sharp  in  that  key,  it 


32  Graded   Lessons    in    Ilarmoni/ 

will  necessarily  be  the  note  to  lose  its  sharp  when  return- 
ing to  the  scale  of  G.  Now  note  especially  that  this 
altered  (in  this  case,  the  restored)  note  is  the  fourth 
degree  of  the  scale  of  G.  Let  us  continue  by  descending 
fifths,  when  by  a  similar  process,  the  scale  having  no 
sharps  will  be  the  scale  of  C.  Further,  the  F-sharp,  which 
is  the  leading  tone  in  the  scale  of  G,  is  altered  (restored) 
to  form  the  fourth  degree  of  the  scale  of  C. 

(7)  Deduction,  While  in  the  ascending  series  the 
added  sharp  always  falls  upon  the  seventh  degree  of  the 
new  scale  or  leading  tone,  in  the  descending  series  the 
one  note  to  be  altered  in  each  case  falls  upon  the  fourth 
degree  of  the  new  scale.  But  since  in  descending  the 
fourth  note  of  the  new  scale  is  the  same  as  the  seventh 
note  of  the  old  scale,  therefore  in  both  cases  it  is  the  same 
note  which  is  altered. 

(8)  Statement  and  Illustration.  Let  us  now  continue 
the  descending  series  of  scales,  notwithstanding  the  fact 
that  there  are  no  more  sharps  to  remove.  Five  notes 
downward  brings  the  note  F  as  the  new  Tonic.  This 
scale,  according  to  §12,  (3)  and  (4),  must  have  B-flat  as 
the  fourth  degree.  Now  notice  that  this  flat  is  introduced 
at  the  point  where  in  the  other  scales  the  sharp  was 
removed.  The  flat  therefore  performs  the  same  office  in 
this  scale  as  was  performed  by  the  removal  of  the  sharp 
so  long  as  there  were  sharps  to  remove.  This  is  like 
the  impecunious  man  who  paid  his  debts,  a  dollar  at  a 
time,  until  his  money  was  all  gone,  and  was  then  obliged 
to  give  his  note  in  further  payment.  It  is  also  illustrated 
by  the  algebraic  proposition  that  the  addition  of  a  minus 
quantity  is  equal  to  the  subtraction  of  a  plus  quantity, 
since  the  addition  of  the  flat  creates  the  same  result  as 
the  removal  or  subtraction  of  a  sharp.  It  is  still  better 
illustrated  l)y  the  register  of  the  thermometer  in  which 
the  key  of  C,  having  neither  sharps  nor  flats,  may  be  com- 
pared to  the  zero  mark,  while  those  keys  with  sharps 
represent  the  corresponding  numbers  of  degrees  above 
zero,  and  the  flat  keys  represent  degrees  below  zero. 
This  is  a  most  important  principle,  for  the  ''relative 
sharpness"  of  different  keys  and  notes  will  be  in  con- 
stant use  after  a  few  lessons. 

(9)  Deduction.  Flats  arc  ihc  ojiposites  of  sharps: 
taking  away  a  sharp  from  a  signature  is  the  equivalent 
of  adding  a  flat,  and  vice  versa. 


Graded   Lessons    in    Ilurmoni/  33 

(10)  Deduction.  As  by  using  double-sharps  a  com- 
plete circle  of  keys  was  formed,  so  by  continuing  as  above, 
by  descending  fi'fths,  using  double-flats  where  necessary, 
a  complete  circle  of  keys  with  flats  may  be  formed,  con- 
tinuing till  D-double-flat  is  reached. 

(11)  Deduction.  Since  keys  having  more  than  six 
sharps  or  six  flats  are  unnecessarily  complicated,  by  uni- 
versal consent  the  first  half  of  the  sharp  circle  is  supple- 
mented by  the  first  half  of  the  flat  circle,  thus  using  the 
simpler  half  of  each,  and  yet  embracing  every  Chromatic 
note. 

(12)  Deduction.  The  question  now  arises,  "Why, 
then,  did  you  go  to  the  extreme  with  what  might  have 
been  a  simple  matter?"  First,  to  show  how  marvelously 
perfect  and  complete  are  the  operations  of  Nature.  Noth- 
ing produced  by  the  finite  mind  of  man  could  result  in 
such  absolute  correspondence,  each  part  proving  the 
whole  by  its  perfect  fitting  with  every  other  part.  There 
is  not  a  flaw  in  the  logic  of  Nature.  It  forms  one  more 
proof  of  the  existence  of  a  higher  power;  and  secondly, 
it  was  carried  to  the  extreme  for  the  reason  that  occa- 
sionally the  more  complicated  keys  are  needed  for  correct 
grammatical  expression.  For  example,  the  Dominant  of 
the  key  of  C-sharp  is  not  A-flat,  but  G-sharp.  In  a 
sonata,  if  the  first  theme  is  in  the  key  of  C-sharp,  the 
second  theme  should  be  in  the  key  of  G-sharp.  Examples 
of  this  are  found  in  Beethoven's  sonatas,  where  the  true 
key  of  a  passage  is  shown  by  about  two  measures  of  many 
accidentals,  followed  by  the  enharmonic  change  into  the 
simpler  corresponding  key. 

(13)  THE  OFFICE  OF  THE  HALF-STEP.  State- 
ment. As  compared  with  the  Major  scale  the  Minor 
scale  is  formed  by  a  different  arrangement  of  the  half- 
steps.  It  will  not  be  possible  to  explain  the  Minor  scale 
in  detail  at  this  time,  but  a  full  exposition  may  be  found 
in  the  text-book  mentioned  above.  It  is  here  particularly 
desired  to  call  attention  to  the  office  of  the  half-step  and 
its  power  in  music.  In  the  case  of  the  ]\Iinor  scale  the 
changed  locations  of  the  half-steps  are  sufficient  to  create 
the  peculiar  Minor  quality.  Further,  in  Collateral  Read- 
ing, §28,  (l)-(3),  the  tendency  notes  are  in  each  case  only 
a  half-step  distant  from  the  note  toward  which  they  are 
drawn,  displaying  a  sort  of  magnetic  attraction.  This 
quality  of  the  half-step  is  further  illustrated  below. 


34  Graded   Lessons    in    Harmon i/ 

(14)  Statement.  The  IMajor  scale  has  been  described 
as  being  made  up  by  the  union  of  two  short  scales  of  four 
notes     each,     called     tetrachords     by     the     Greeks — thus 

1234     567  8.      Notice    that   the   half-step    concludes 

each  tetrachord.  Upward  scales  always  conclude  with  a 
half-step,  to  give  the  feeling  of  completion. 

(15)  Deduction.  A  Major  scale  is  composed  of  two 
tetrachords.  The  last,  or  upper,  tetrachord  of  one  scale 
becomes  the  first  tetrachord  of  the  scale  having  one  more 
sharp. 

(16)  Deduction.  Similarly,  or  conversely,  the  first 
half  of  one  scale  becomes  the  last  half  of  the  scale  having 
one  less  sharp.  These  two  deductions  show  still  more 
completely  the  intimate  relations  of  the  scales. 

The  study  of  the  scales  reveals  the  wonderful  order, 
symmetry  and  perfection  of  the  simple  laws  of  Nature. 

40.  XoTE.  The  scale  appears  to  be  the  very  epitome  of  key 
relations  as  well  as  of  the  wonderful  tone  relations  and 
qualities  expressed  in  itself.  Let  me  explain  my  meaning 
in  detail.  You  have  learned  how  there  are  six  keys  related 
to  any  given  key,  viz :  the  Dominant  and  Sub-dominant  Ma- 
jor, the  Relative  Minors  of  all  three  (that  is,  including  the 
Tonic  as  well  as  the  Dominant  and  Sub-dominant)  and  fur- 
ther, the  Tonic  IMinor.  Let  us  see  how  this  works  out  in 
the  scale  of  C.  Please  take  a  piece  of  paper  and  write  on  it 
the  letter  names  of  the  scale  tones  as  follows :  C,  D,  E,  F,  G, 
A,  B,  C.  If  you  like,  you  may  omit  the  last  C,  which  is 
merely  a  duplicate  of  the  keynote.  Xow  check  off  from  this 
list,  the  Tonic,  Sub-dominant  and  Dominant  and  you  have 
the  three  keys  representing  the  Major  group.  Xow  check  off 
the  Relative  Minors :  first,  of  C.  which  is  A ;  next,  of  F, 
which  is  D;  last,  of  G,  which  is  E.  Xow  we  find  everything 
checked  off,  except  the  seventh  or  leading  tone;  let  us  lay 
aside  the  consideration  of  this  leading  tone  for  a  moment.  We 
may  say  in  passing  that  the  Tonic  Minor  is  not,  strictly 
speaking,  a  related  key,  but  is  rather  the  same  key  with  a 
change  of  mode.  Let  us  look  at  results:  we  have  three 
Major  and  three  Minor  keys;  that  is,  each  Major  has  its 
Relative  Minor.  .Tt  seems  to  me  almost  like  dividing  the 
key  in  perfect  balance  between  the  masculine  and  feminine. 
Xow,  further,  if  you  understand  just  a  little  of  chord  build- 
ing, and  I  am  sure  you  do,  if  you  build  the  simple  triads 
upon  C,  F  and  G,  you  will  find  that  in  this  key,  C,  they  are 
Major  chords;  whereas  the  triads  built  upon  the  Relative 
Minors,   D,  K,  and  A,  form  Minor  chords.     So  here  we  lind 


(traded    Lessons    in    Ifarmoiii/  35 

a  correspondence  /;/  the  key  between  its  Major  cliords  and 
the  related  Major  keys;  and  between  its  Minor  chords  and 
the  Minor  related  ke3S.  Can  you  not  see  how  the  key  in  its 
content  is  a  wonderful  epitome  of  the  whole  scheme  of  key 
relationship?  This  is  to  me  one  of  the  most  wonderful 
and  beautiful  things  in  the  subject  of  Theory. 

But  now  you  question :  "How,  then,  do  you  account  for 
the  oversight  in  the  case  of  the  seventh  degree?"  The  answer 
is  this:  "The  seventh  degree  is  the  variable  one,  or  the  point 
from  which  the  key  reaches  out  toward  other  keys.  You  will 
remember  that  in  each  case  it  is  a  leading  tone  wdiich  is  cre- 
ated or  destroyed  in  going  upward  or  downward  in  our  circle 
of  keys:  and  so  Nature  left  out  this  tone  as  the  changeable 
one  in  tlie  scheme  of  representing  the  great  relationships  of 
music,  through,  and  in,  the  scale. 

41.  QUESTIONS  21-27,  Key.  p.  14. 

Remark:  Teachers  will  find  the  "Topics  for  Discus- 
sion" at  the  end  of  each  chapter  of  "Key"  of  suggestive 
value    for   classroom   work. 

DAILY   TECHNIQUE    DRILL. 

Motto — //  "Theory  and  Practice  go  together'  he  sure  to 
let  Practice  go  with  this  Theory. 

42.  SPECIAL  DIRECTIONS. 

After  completing  the  study  of  a  subject,  do  not  drop 
it,  but  continue  to  spend  a  few  minutes  daily  in  keeping  it 
in  mind,  with  the  aid  of  this  DAILY  DRILL. 

Take  one  or  two  keys  each  day,  never  less  than  one. 
This  will  complete  the  circle  of  keys  in  one  or  two  weeks, 
giving  real  Facility. 

Specific  Names. 

(1)  (a)  Xame  and  play  the  notes  roi)rcsenling  the 
specific  scale  names,  in  the  following  order :  Tonic,  Octave, 
Super-tonic,  Leading  Tone,  Mediant,  Sub-mediant,  Sub- 
dominant,  Dominant. 

NoTK.  This  order  will  nut  lie  difficult  to  remember,  if 
it  be  noticed  that  the  successive  tones  start  as  far  as  possi- 
ble from  each  other,  and  approach  as  closely  as  possible, 
giving'  the  order  1,  S,  2,  7,  3,  6,  4,  5. 

To  illustrate  the  above,  in  the  key  of  D.  The  student 
will   recite   (and  play)    as   follows:  Tonic,  D ;  Octave,   1); 


36  Graded   Lessons    i)i    Ilarmoni/ 

Super-tonic,   E ;    Leading   Tone,   CS ;   ]\Iediant,   ¥^ ;    Sulj- 
mediant,  B ;  Sub-dominant,  G ;  Dominant,  A. 

(b)   Recite  the  above  without  reference  to  a  key- 
board. 

(2)  Repeat  the  above  in  the  Parallel  ]\Iinor  kej'. 

(3)  Comparing  the  Major  and  the  Harmonic  Elinor 
forms  of  the  scale  we  are  now  considering,  state  which 
notes  of  the  Major  scale  are  lowered  to  make  the  ISIinor 
form. 

(4)  Name  and  touch  scale  notes  in  the  following 
order  :  1,  6,  4,  2,  5,  3,  1.  Learn  this  order  by  heart.  Some- 
times vise  the  specific  names  instead  of  the  numerals. 

To  illustrate  in  the  key  of  D  as  above,  the  student  will 
play  the  notes  as  he  says,  "1  (or  Tonic)  is  D ;  6  (or  Sub- 
mediant)  is  B;  4  (or  Sub-dominant)  is  G" ;  etc. 

(5)  Recite  the  sharps  in  the  order  found  in  the  signa- 
ture.    Recite  the  flats  in  the  order  found  in  the  signature. 


Graded   Lesxoiix    in    Ilarmoui/  37 


LESSON  5. 

INTERVALS.* 

Motto — By  the  study  of  intervals  the  inner  meaning  aud 

the  uses  of  chords    are  revealed.     By  it  ive  reach 

the    heart  of  music. 

General  Names. 

43.  STUDY.     Read  and  study  daily  H.  S.,  §§53-r.r :  Kev, 
56,  and  Collateral  Reading.  ^4C^,  {:])-( r,). 

EXERCISES. 

Referring  to  the  sections  above  mentioned,  the  student 
will,  according  to  his  advancement,  go  through  all  re- 
quired exercises,  first  at  the  keyboard  and  then  in  writing; 
or  he  will  take  a  part  at  the  keyboard  and  the  rest  in 
writing.  In  any  case,  they  should  be  continued  until 
facility  is  attained. 

RECITATIOX. 

It  will  assist  the  power  of  quick  thinking  to  recite  a 
few  of  the  exercises  to  a  friend ;  or  to  recite  without  a 
listener,  by  setting  the  metronome  at  a  slow  speed  and 
naming  one  note  of  the  required  interval  with  each  beat, 
or  by  giving  the  correct  answer  to  a  question  within  a 
certain  limited  number  of  beats. 

44.  EAR-TRAINIXG. 

Following  the  directions  given  in  //.  S..  §81  et  scq.. 
work  as  well  as  you  can  by  yourself  or  with  the  help  of 
another. 

Use  particularly  the  Ear-training  Exercises,  realizing 
that  when  you  sing  two  tones  in  succession  a  melodic 
interval  is  formed.  Realize  also  that  intervals  are  (usu- 
ally) made  from  the  natural  scale  tones. 

♦Special  Note.  In  taking  up  this  subject  it  is  well  lo  observe  that  it  is 
divided  into  four  general  sections,  which  at  first  are  studied  rather  independently 
of  one  another,  viz.:  (1)  The  General  Names  of  Intervals;  (2)  The  Specific 
Names;      (,S)   Inversions;      (4)   Consonant  and    Dissonant    Intervals. 

Try  to  keep  these  four  linos  of  study  distinct  in  the  mind. 


•Vo  'B'^l 


38  Graded   Lessons    in    Ilarmoni/ 

Special  Note.  Seconds  and  sevenths  are  harsh  disso- 
nances :  we  can  hardly  help  discerning  them.  Thirds  and 
sixths  suggest  a  chord  by  their  mellow  consonance. 

The  sixth  is  distinguished  easily  from  the  third :  it  is 
much  further  apart.  Fourths  and  fifths  both  sound  "empty" : 
note  how  the  fifth  "warms  up"  when  the  third  is  added. 

Fifths  remind  one  of  tuning  a  violin — the  effect  of  the 
open  strings. 

The  fourths  suggest  a  cavalry  call  on  a  horn. 

A  imison  is  a  single  tone. 

An  octave  is  a  tone  and  its  "shadow" — not  something  dif- 
ferent,   but    still    slightly    "brightened"    by    the    higher    pitch. 

Keep  these  in  mind  in  ear-training  and  ask  yourself:     "Is 
it   a    sharp    dissonance?"     If    not    it    cannot    be    a    second    or 
seventh.     (Note.  One  is  the  inversion  of  the  other,  hence  they 
are  both  in  the  same  class.)     "Does  it  sound  empty?"     If  not, 
it   is  neither  a   fifth  nor  fourth    (again   inversions — therefore 
in   the   same  class).     So   you   eliminate  them  two  at   a   time, 
till  you  can  answer  "yes"  to  the  question 
Is  it  harsh  ? 
Is  it  empty? 
Is  it  sweet  like  a  chord? 

45.  QUESTIONS  1-10,  Key.  p.  23. 

COLLATERAL    READING. 

46.  (1)  The  office  of  the  intervals  is  seldom  formally 
stated;  it  is  this:  As  chords  are  composite,  being  made  up 
of  several  intervals,  the  character  of  a  chord  must  neces- 
sarily depend  upon  the  character  of  its  intervals.  The 
best  approach  to  a  true  understanding  of  chord  structure 
is  therefore  through  the  study  of  intervals.  The  exposi- 
tion here  given  differs  radically  from  accepted  methods, 
the  attempt  being  made  to  reach  results  of  practical  value 
through  an  appeal  to  the  reason  instead  of  to  the  memory. 

(2)  Statement.  An  interval,  in  the  physical  sense,  is 
an  expression  of  distance  between  two  given  tones  sound- 
ing either  together  or  in  immediate  succession.  Artis- 
tically, it  is  the  effect  produced  by  the  two  tones.  While 
it  is  necessary  to  a  discussion  of  the  subject  to  refer 
almost  exclusively  to  the  physical  interval  the  student 
should  continually  think  also  of  the  effect  or  artistic  result. 

When  the  two  tones  of  an  interval  sound  together,  it 
is  called  an  harmonic  interval;  when  sounding  in  succes- 
sion, it  is  called  a  melodic  interval. 


(Iradcd   Lessons    In    Harmony  39 

GENERAL  NAMES  OF  IXTER\'ALS. 

(3)  Statement.  The  general  name  of  an  interval  is 
determined  by  the  number  of  degrees  of  the  staff  included 
in  its  extent,  counting  extremes,  or  degrees  upon  which 
the  notes  stand,  as  well  as  those  between,  e.g.,  C-A  (the 
lower  note  is  mentioned  first)  is  a  sixth,  since  six  degrees 
are  involved;  G-B  is  a  third,  etc. 

(4)  Exercises,  (a)  Name  the  following  intervals: 
F-B;  B-D;  E-D  ;  C-B  ;  D-F  ;  B-F  ;  B-G;  A-G  ;  G-A  ;  A-C. 
(The  answers  are,  respectively,  a  fourth,  third,  seventh, 
seventh,  third,  fifth,  sixth,  seventh,  second,  third.) 

(b)  First  at  the  keyboard  and  afterward  in  writing, 
form  the  intervals  of  a  sixth,  third,  fifth,  seventh,  second, 
fourth  and  ninth  from  each  of  the  following  notes:  F,  A, 
D,  G,  B,  E  and  C. 

(c)  Describe  the  intervals  found  in  the  chord 
G-B-D-F.  Ans.  G-B  is  a  third,  G-D  a  fifth,  and  G-F 
a  seventh;  B-D  is  a  third,  B-F  a  fifth,  and  D-F  a  third. 
(These  intervals  are  found  by  taking  the  different  notes 
in  turn  and  considering  in  connection  with  those  above.) 

Similarlv,  describe  the  intervals  found  in  the  chord 
A-C-F  ;  in  the  chord  F-G-B-D ;  F-B-D ;  F-A-C-D. 

(d)  Describe  the  intervals  found  in  the  various  chords 
in  printed  music ;  for  example,  in  a  hymn  tunc. 

(5)  Statement.  The  presence  or  absence  of  sharps 
and  flats  does  not  affect  the  general  name  of  an  interval, 
though  the  specific  name  may  be  changed,  as  will  be  seen 
later. 

(6)  Statement.  Extended  Intervals.  Duplication  of 
Notes.  When  the  notes  of  an  interval  are  more  than  an 
octave  apart  they  are  considered  just  as  if  they  were  in 
the  same  octave.  In  Theory  neither  distance  nor  duplicates 
of  notes  affect  the  result.  The  relationships  are  taken  as 
those  of  the  seven  notes  of  the  scale,  irrespective  of  pitch 
or  duplication.  The  chief  exception  to  this  is  the  interval 
of  the  ninth,  which  in  the  chord  of  the  ninth  needs  to 
stand  at  the  full  distance  from  the  root  of  the  chord. 


40  Graded  Lessons   in   Jlarmonj^ 

LESSON  6. 

INTERVALS  (Cont.) 

Specific  (or  Descriptive)   Names.     Measurement  of 
Intervals. 

47.  Following  the  plan  outlined  in  preceding  lessons,  study 
the  matter  in  H.  S.,  §§58-09;  in  the  Key,  §§58-09;  and  in 
Collateral  Reading,  §51. 

KEYBOARD  DRILL  as  outlined  in  //.  S.,  Key  and 
Collateral  Reading. 

WRITTEN  EXERCISES  as  outlined  in  H.  S.,  the 
Key  and  Collateral  Reading. 

N.B.  Do  not  lose  sight  of  the  General  Xame  of  the  inter- 
vals when  studying  the  Specific  Names. 

Special  Note.  Here  is  a  very  simple  view  of  the  Normal 
intervals.  Comparing  the  interval  C-G  and  the  interval  C-A, 
the  first  is  a  Perfect  fifth  and  the  second  is  a  Major  sixth. 
But  why?     Here  is  the  answer: 

First  take  the  notes  of  the  interval  C-G.  The  letter  G 
belongs  to  the  scale  of  C  Major,  therefore  the  interval  is 
Normal.  Now  let  us  reverse  the  test :  does  C  belong  to  the 
scale  of  G  Major?  We  find  that  it  does;  and  since  each 
letter  belongs  to  the  other's  scale,  we  say  that  the  interval 
is  Perfect  as  well  as  Normal. 

Now  let  us  try  the  interval  C-A.  A  belongs  to  the  scale 
of  C,  therefore  the  interval  is  Normal.  But  the  reverse  is 
not  true,  for  C  does  not  belong  to  the  scale  of  A  Major  (Clf 
being  the  required  note).  Therefore  we  say  that  C-A  is  a 
Normal  interval,  because  the  upper  note  belongs  to  the  scale 
of  the  lower  note;  but  it  is  not  a  Perfect  interval,  since  the 
lower  note  does  not  belong  to  the  Major  scale  of  the  upper 
note.     From    the   above   we   can   deduce   these    rules : 

Considering  any  given  interval,  if  the  upper  note  belongs 
to  the  Major  scale  of  the  lower  note,  the  interval  is  at  least 
Normal;  and  if  the  lower  note  also  belongs  to  the  Major 
scale  of  the  upper  note,  the  interval  is  also  Perfect.  In  other 
words,  when  the  relationship  is  Normal  in  both  directions. 
it  is  the  most  complete  relationship  possible,  and  the  interval 


Graded    T.cssotis    in    llarmonij  41 

is  called  Perfect;  but  when  tin  k  lalioiibliip  is  Xormal  in 
only  one  direction  (when  oidy  (iiic  belongs  to  the  scale  of 
the  other),  the  relationship  is  not  so  complete  and  the  intervals 
are  not  called  Perfect,  but  simply  ^Nlajor. 

48.  EAR-TRAINING. 

Form  with  the  voice  INIajor  thirds,  starting  in  turn 
from  each  (chromatic)  degree  within  the  octave. 

After  working  for  a  few  days  with  Major  thirds,  try 
in  turn  Minor  thirds.  Perfect  fourths,  Perfect  fifths, 
Major  sixths,  Minor  sixths,  Major  sevenths,  Minor  sev- 
enths and  Perfect  octaves.  Let  this  drill  be  carried 
through  possibly  six  months. 

Please  note  that  this  drill  has  to  do  with  intervals  in 
abstract;  that  is,  having  no  relationship  to  any  key.  For 
some  musicians  it  is  difficult  to  dissociate  the  tones  from 
Key  Sense,  but  it  is  a  very  desirable  power  to  have.  It 
is  curious  that  with  an  unmusical  person  we  have  to 
labor  a  long  time  to  create  this  sense  of  Key  Relationship 
(for  they  hear  almost  nothing  of  it)  ;  and  then  that  we 
reverse  the  process  and  try  to  dissociate  the  hearing  of 
tones  from  Key  Sense,  in  order  to  measure  them  more 
accurately. 

Note.  In  this  chapter  try  to  make  no  break  in  the  daily 
study,  as  it  is  desirable  to  gain  a  complete  view  of  the  subject 
as  soon  as  possible  after  undertaking  it.  The  daily  drill  in 
Lesson  8  will  fix  the  matter  in  the  mind  and  insure  facility 
if  it  should  seem  difificult  at  first. 

Remember  that  this  is  foundation  zvork,  and  that  the  prin- 
ciples here  developed  will  be  used  alzcays. 

49.  QUESTIONS  11-21,  Key.  pp.  23,  25,  26. 

50.  ANSWERS   TO   QUESTIONS   11-21,   Kc\,   pp.   23, 
25,  26. 

(11)  The  terms  Major,  Minor,  Diminished  and  Aug- 
mented may  be  called  "comparative"  or  "'descriptive" 
terms,  since  by  them  we  may  compare  or  describe  the 
various  forms  possible  to  any  given  interval. 

(12)  The  Major  is  the  standard  of  comparison,  for 
we  say:  "The  ]\Iinor  is  one  half-step  smaller  than  Ma- 
jor," etc, 

(13)  A    Normal    interval    is    an    interval    formed    by 


42  Graded   Lessons   in    Harmon  if 

taking  the  first  degree  of  any  Major  scale  in  connection 
with  any  degree  of  the  same  scale. 

(14)  A  simple  way  of  measuring  intervals  is  as  fol- 
lows: Compare  with  the  Normal  intervals,  using  the  lower 
note  as  a  Tonic.  This  is  more  particularly  described  in 
H.  S.,  §§  59-62,  also  §§  65-67. 

(15)  The  following  intervals  are  called  Perfect  when 
Normal :  primes,  fourths,  fifths  and  octaves. 

(16)  A  convenient  way  of  remembering  which  are 
Perfect  intervals  is:  (1)  Think  of  the  nearest  related 
keys  (Dominant  and  Sub-dominant),  remembering  that 
the  octave  is  merely  a  duplication  of  the  Tonic.  An- 
other way  for  more  advanced  students  to  remember  is 
to  think  of  the  chief  chords  of  a  key.     Read  Key,  75  (a). 

(17)  The  Normal  Major  intervals  are  seconds,  thirds, 
sixths  and  sevenths. 

Note.  Both  the  Perfect  and  the  Major  intervals  are  more 
easily  remembered  by  observing  tliat  they  occur  in  pairs;  or, 
in  other  words,  in  complementary  groups  as  follows:  (a) 
Perfect  intervals:  Unisons  and  octaves,  fourths  and  fifths; 
(b)   Major  intervals:  seconds  and  sevenths,  thirds  and  sixths. 

(18)  The  opinion  of  the  writer  is  that  Perfect  inter- 
vals may  be  considered  in  practical  theory  as  a  subdivi- 
sion, rather  than  radically  different  from  Major  inter- 
vals, since  they  are  equally  normal. 

(19)  Two  reductions  are  required  to  change  Major 
intervals  to  their  Diminished  form. 

(20)  One  reduction  is  required  to  change  Perfect  in- 
tervals to  their  Diminished  form. 

(21)  In  this  respect  the  Perfect  intervals  may  be  said 
to  differ,  in  that  thev  have  no  ]\Iinor  form.  Read  Key, 
76. 

COLLATERAL    READING. 

51.  (1)  Statement.  Chords  are  dependent  upon  their 
component  intervals  for  their  names,  as  "chord  of  the 
sixth,"  "of  the  six-four,"  etc.  Chords  are  similarly  de- 
pendent upon  their  intervals  for  their  qualities,  as  Major, 
Minor,  Diminished  or  Augmented,  being  often  named 
from  the  most  characteristic  interval  contained.  There 
are  then.  Major,  Minor,  Diminished  and  Augmented  in- 


Graded   T.rsxons-    in    Ilnrmnni/  43 

tcrvals.  The  Majur  interval  is  taken  as  unit  of  com- 
parison, Minor  meaninj?  an  interval  a  half-step  smaller 
than  the  Major;  Diminished,  still  smaller;  and  Augmented 
meaning  larger  than  Major.  I'^ormally  stated,  and  more 
accurately,  the  various  intervals  are: 

Major  1    .|.|^^    standard  of    measurement. 
Perfect ) 

(The  difference  between  the  two  is  explained  below.) 

Minor,  meaning  less  by  a  half-step  than  Major. 

Diminished,  meaning  still   loss,   or   less   Ijy   a  half-step 
than    Minor   or    Perfect. 

Augmented,  meaning  increased,  or  greater  l)y  a  half- 
step  than  Major  or  Perfect. 

XoTK.  A  momentarily  helpful  explanation  of  the  term 
"Perfect"  is  that  "those  Major  intervals  which  have  no  Minor 
form  are  called  Perfect."  A  more  accurate  statement  is  that 
"those  .\ormal  intervals  which  have  no  Minor  form  are 
called  Perfect."  But  the  meaning  of  the  word  Normal  is 
not  yet  clear,  and  the  chief  point  at  present  is  to  consider 
Perfect  intervals,  not  as  essentially  different  from  Major, 
but  as  a  sub-division  of  the  same  class,  the  full  distinction 
to  be  seen  later.  Just  now  tliink  of  them  as  "those  which 
have  no  Minor  form." 

^lEASUREMEXT   OF   IXTERVALS. 

(2)  The  older  way  of  measuring  intervals  is  to  count 
the  half-steps  included  in  their  extent,  first  memorizing 
the  number  of  half-steps  in  each  of  the  different  inter- 
vals— a  feat  too  difficult  for  the  average  person.  The 
following  is  offered  as  a  simple,  practical  and  valuable 
method,  involving,  as  it  does,  a  constant  comparison  of 
the  different  forms  of  the  intervals. 

(3)  Statement.  The  Standard  of  Measurement.  Con- 
sider the  scale  of  C  upon  the  keyboard.  From  C  to  any 
other  degree  of  the  scale  of  C  Major,  or  from  C  to  any 
white  key,  is  a  Major  or  a  Perfect  interval,  i.e.,  a  Normal 
interval  •  e.g.,  the  following  are  all  Normal  intervals : 
C-D;  C-E:  C-F;  C-G;  C-A ;  C-B;  C-C.  Some  of 
these  are  Major  intervals  and  some  are  Perfect,  but 
all  are  Normal.  This  gives  us  a  practical  standard  of 
measurement,   by   which    any   interval   can   be    measured 


44  Graded   Lessoii.s    in    Ilarmoui/ 

and  its  quality  determined;  for  by  the  definitions  above, 
a  Minor  interval  is  a  half-step  smaller  than  a  Major  in- 
terval, an  Augmented  a  half-step  larger  tha^  the  Major, 
etc.  To  illustrate:  C-A  is  a  Major  sixth;  one  half-step 
less,  or  C-Ab,  is  a  Elinor  sixth.  When  reduced  again  by 
a  half-step,  to  either  C-Abb  (double-flat)  or  CJf-Ab 
(for  either  the  upper  or  lower  note  may  be  altered),  it 
becomes  a  Diminished  sixth.  Again,  compared  with  the 
Major  form,  by  increasing  the  distances  by  one  half- 
step  an  Augmented  sixth  is  formed,  C-AJf.  (Note.  The 
Diminished  sixth  is  seldom  used  in  composition ;  it  is 
found  here  only  for  illustration.)  For  exercises  see  (7) 
below. 

(-i)  Major,  Perfect,  Minor,  Diminished  and  Aug- 
mented are  comparative  terms,  being  considered  in  re- 
lation to  the  Normal,  or  standard  of  measurement. 

(5)  Statement.  From  the  note  C  to  any  note  of  the 
scale  of  C  is  a  Normal  interval.  Similarly,  from  the  key- 
note of  any  Major  scale  to  any  note  of  the  same  scale,  is 
just  as  Normal,  since  the  scales  are  simply  duplicates  one 
of  the  other.  (See  §12.)  For  example,  from  F  to  any 
note  of  the  scale  of  F  is  a  Normal  interval ;  from  D  to 
any  note  of  the  scale  of  D,  or  from  Bb  to  any  note  of 
the  scale  of  Bb,  is  a  Normal  interval.    Therefore: 

(G)  Statement,  (a)  To  form  any  required  interval, 
ask:  "What  would  be  the  Normal  interval?"  Count  from 
the  lower  note,  and  then  modify  this  Normal  note  as  may 
be  required. 

(b)    To  describe  a  given  interval,  find  the  Normal 
interval,  as  above,  and  compare  it  with  the  given  interval. 

Illustration  of  (a).  "Form  an  Augmented  sixth  from 
E.''  Process:  "The  Normal  sixth  from  E  would  be  the 
sixth  degree  of  the  scale  of  E  Major,  which  is  Ot.  As  an 
Augmented  sixth  is  a  half-step  larger  than  the  Normal,  it 
must  be  E-Cx  (double-sharp). 

Illustration  of  (b).  "Describe  the  interval  D-Bb." 
Process:  "The  general  name  of  this  interval  is  a  sixth; 
the  Normal  sixth  from  the  lower  note,  D,  is  B^.  As 
the  given  interval  is  a  half-step  smaller  it  must  be  a  Minor 
sixth."  (N.B.  (8)  shows  that  the  Normal  sixth  is 
Major,  and  therefore  has  a  Minor  form. 

(7)  Exercises,  (a)  E-C#  is  a  Major  sixth.  Change 
it  first  to  a  Minor,  anfl  then  to  an  .Augmented  sixth.   (Ans. 


Graded   Lessous   in   Ilarinoni/  45 

The  Minor  sixth  from  E  is  E-C= ;  the  Augmented  sixth  is 
E-Cx.)  Change  the  Major  third  F-A  to  a  Minor  third. 
Change  the  jNIajor  sixth  F-D  to  an  Augmented  sixth. 
Change  the  Augmented  second  D-EJf  to  a  Major  second; 
to  a  Minor  second. 

(b)  Form  an  Augmented  sixth  from  F ;  from  A; 
from  C ;  from  D  ;  from  G ;  from  B.  From  the  same  notes 
fofm  Augmented  fourths;  also  Augmented  fifths. 

(8)  Statement.  The  Perfect  intervals  are  the  Nor- 
mal unisons,  fourths,  fifths  and  octaves.  (Note.  This 
statement  should  be  memorized.  It  will  appeal  to  the 
memory  better  by  noting  that  the  unison  and  octave  are 
complementary  intervals,  as  are  also  the  fourth  and  fifth. 
Further,  it  should  be  observed  that  these  intervals  cor- 
respond to  the  chief  tones  of  the  scale,  namely,  the  Tonic, 
Sub-dominant  and  Dominant — the  octave  being  in  scale 
study  the  duplicate  of  the  Tonic.)  These  figures,  one, 
four,  five  and  eight,  representing  the  Perfect  intervals, 
and  also  the  chief  tones  of  the  scale,  will  be  very  fre- 
quently under  consideration. 

The  Major  intervals  are  Normal  seconds,  thirds, 
sixths  and  sevenths.  Observe  that  the  seconds  and  sev- 
enths are  complementary,  as  are  the  thirds  and  sixths. 
There  are  then  two  pairs  of  Perfect  intervals  and  two 
pairs  of  Major  intervals,  if  two  complementary  intervals 
are  taken  as  a  pair. 

(9)  Exercise,  (a)  State  whether  the  following  inter- 
vals are  Normal,  and  if  so,  whether  Major  or  Perfect. 
Further  describe  these  which  are  not  Normal,  as  Minor, 
Diminished,  or  Augmented  ;  C-G  ;  C-D  ;  D-C  ;  E-B  ;  B-F  ; 
B-E;  E-F;  F«-A«;  FJf-B ;  Ft=.-C;  A-F ;  A-E ;  A-Clt;  F-Bb  ; 
F-A  ;  F-D  ;  F-Eb. 

(b)  Form  a  Major  sixth  (upward)  from  each  of 
the  following  notes  :  D  ;  G  :  C  ;  F  ;  B  ;  CC  ;  Eb  ;  D»  ;  Ab  ;  Gb. 

(c)  Form  Augmented  fourths  from  the  same 
notes;  also  Diminished  fifths.  Augmented  sixths  and 
Minor  sevenths. 

(d)  Form  a  Major  third  from  1),  and  change  to  a 
Minor  third. 

Form  a  Major  sixth   from   E,  and  change  to  an 

Augmented  sixth. 
Form  a  Perfect  fifth  from  Fi,  and  change  to  an 

Augmented  fifth. 


46  Graded  Lessons   in   Harmony 

Form  a  Perfect  fourth  from  Bb,  and  change  to  a 
Diminished  fourth. 

(e)  Describe  each  interval  in  the  following  chords: 
C-E-G-Bb ;  Ab-C-E-F« ;  C-D-FS-A ;  B-D-F-Ab ;  GS-B-D-E. 

(f)  Similarly  describe  chords  seen  in  your  daily  mu- 
sical experience.  (Make  this  your  daily  practice  until 
facility  is  acquired.  He  who  would  attain  real  familiarity 
and  facility  with  chords  in  analysis  and  at  the  keyboard 
must  first  acquire  the  power  suggested  by  these  exercises.) 


Graded  Lessons   in  Harmony  47 

LESSON   7. 

INTERVAl.S   (Cont.) 
Inversions  in  General. 

52.  STUDY:   H.  S.,  §§70-72;  Addendum   to   §72,   p.  42; 
and  Collateral  Reading.  §58   (1 )-(()). 

KEYBOARD  EXERCISES. 

Take  the  exercise  in  §70  of  H.  S.,  and  play  each  inter- 
val, giving  the  general  name  as  it  is  played,  and  then  play 
it  inverted,  giving  the  general  name  of  the  inversion. 

Continue  this  exercise  by  taking  intervals  from  other 
keys,  remembering  that  the  addition  of  sharps  or  flats  can 
never  alter  the  general  name  of  an  interval. 

RECITATION. 

Recite  the  aliove  or  similar  exercises. 

Inversion  of  Specific  Intervals. 

53.  STUDY.     Read  and  studv  dailv,  //.  i^.  §§73-74,  and 
Collateral  Reading,  §58,  (7)-(10). 

KEYBOARD  EXERCISES. 

(a)  Play  the  interval  D-FS ;  describe  it  (that  is,  give 
its  specific  name)  ;  invert  it,  and  describe  the  inversion. 
(Illustration:  The  general  name  of  this  interval  is  a  third, 
since  three  letters  are  involved.  The  specific  name  is  a 
Major  third,  since  F$  is  the  Normal  third  in  the  scale  of 
D.  (Remember  th;.t  we  "think"  in  the  scale  of  the  lozi'er 
note.)  Inverted,  the  general  name  will  be  a  sixth 
(!) — 3=(I)  :  and  the  s])ecificd  name  will  be  a  Minor  sixth, 
since  a  Major  interval  becomes  Minor  when  inverted.  To 
l)rove  that  this  is  a  Minor  sixth,  by  thinking  in  the  scale 
of  the  lower  note  we  will  find  l)if  to  be  the  Normal  sixth 
from  Vt  (remember  that  Vt  is  now  the  lower  note),  and 


48  Graded  Lessons   in   Harmonij 

therefore  the  Major  sixth  from  FJf.  Xow  as  D  is  a  half- 
step  nearer  to  the  lower  note,  the  interval  FS-D  is  a  Minor 
sixth.  Hence,  we  may  conclude  that  D-FS  is  a  Major 
third,  which  inverted  becomes  F--D,  a  Minor  sixth.) 

(b)  Proceeding  as  in  the  above  illustration,  take  each 
of  the  following  intervals,  describe  it,  then  invert  and  de- 
scribe the  inversion  (the  lower  note  of  the  interval  is 
mentioned  first):  E-C :  G-B ;  G-C ;  G-E;  G-F;  G-Ftf; 
C-A;  C-Ab;  C-Bb;  F-GJ ;  F-Ab  ;  F-B;  F-D;  F-DS;  F-Eb  ; 
D-DS;  F«-C*;  Dl-Cfi;  C»-Bb ;   D?-G;  Db-G;  D-Eff;  G«-F. 

54.  WRITTEN  EXERCISES. 

Write  the  more  difficult  of  the  preceding  exercises, 
particularly  those  of  which  you  are  not  absolutely  sure. 
Write  at  least  one  complete  description,  following  the 
foregoing  illustration.  In  all  of  these  written  exercises 
describe  carefully  the  interval  and  its  inversion. 

RECITATIOX. 

Recite  some  of  the  above  with  the  metronome  as  pre- 
viously suggested. 

55  EAR-TRAINIXG. 

Continue  the  study  of  the  different  intervals  (see  H.  S., 
§§87-88).  The  help  of  another  person  is  valuable  at  this 
point.  If  it  cannot  be  obtained,  try  to  concentrate  the 
attention  upon  the  quality  or  character  of  the  different 
intervals  as  you  strike  them  at  the  piano.  Also  try  to 
sing  the  intervals — for  example,  taking  the  note  C  from 
the  piano,  try  to  sing  the  Major  Third  and  then  the  Minor 
third.  Proceed  similarly  with  other  intervals.  Also  learn 
to  listen  to  the  quality  of  the  different  intervals  and  so  dis- 
tinguish them.  This  will  be  more  fully  treated  in  the 
next  lesson. 

5G.  QUESTIOXS  22-29,  Key,  p.  20. 

Special  Note.  The  usual  cause  of  failure  to  grasp  and 
use  the  specific  intervals  and  inversions  is  that  wc  forget 
to  "think"  in  the  scale  on  the  loiver  note.  If  you  have  trouble 
at  this  point,  reread  carefully  //.  S.,  §§59-62,  and  Key,  59,  62. 

.-,7.  AXSWER  TO  QUESTION  22,  Key.  ]..  20. 

Extended  Intervals  are  those  in  which  the  two  tones 
are  more  than  an  octave  apart,  being  considered  as  dupli- 


(haded    Lessons    hi.    Ilttrvioni/  49 

cations  or  extensions  of  similar  intervals  within  the 
octave.  Their  relationships  are  precisely  the  same  as  in 
the  cases  of  their  smaller  forms.  Conseqnently,  through 
the  action  of  this  principle,  when  we  construct  a 
large  chord  (even  covering  many  octaves,  as  in  the  cases 
of  the  orchestra  or  grand  organ)  no  new  principles  are 
introduced  and  no  new  relationships  are  developed.  On 
the  contrary,  the  chord  is  considered  merely  as  an  enlarge- 
ment of  the  simple  form,  resulting  from  the  duplication 
of  notes  in  several  octaves.  (To  analyze  such  a  chord 
this  simple  rule  will  suffice:  Place  all  notes  within  the 
compass  of  one  octave,  strike  out  duplicates  of  all  letters, 
and  so  reduce  the  chord  to  its  simplest  form.) 

ANSWER  TO  QUESTION  25,  Key,  p.  20. 

This  question  is  intended  to  bring  out  the  wonderful 
quality  of  chords,  in  the  following  respect :  that  when 
inverted  they  do  not  change  their  real  quality,  in  spite 
of  the  fact  that  by  inversion  all  the  Major  intervals  in  the 
chord  become  Minor  intervals,  all  the  Diminished  become 
Augmented,  and  vice  versa.  To  illustrate  more  clearly, 
let  us  take  the  triad  C-E-G  and  invert  it,  so  that  it  be- 
comes E-G-C.  Now  observe  that  the  Major  interval  C-E 
of  the  first  form  becoines  Minor  E-C  in  the  inverted  form. 
Now  observe  that  the  chord  E-G-C  is  just  as  much  Major 
now  as  it  was  in  the  original  form,  C-E-G.  This  brings 
us  to  the  thought  that  it  is  not  mere  presence  of  the  Major 
or  Minor  interval  in  the  chord  which  makes  that  chord 
Major  or  Minor,  but  it  is  the  relation  of  each  tone  in  the 
chord  to  the  root,  which  gives  the  real  character  to  the 
chord.  This  correlative  quality  of  intervals,  by  which  a 
Major  third  may  become  a  Minor  sixth  and  yet  not  give 
a  Minor  quality  to  the  chord,  is  one  of  the  most  wonderful 
provisions  of  Nature.  Without  this  quality  we  would  be 
entirely  unable  to  use  chords  in  their  various  inversions 
and  positions,  for  every  new  form  would  necessarily  give 
a  new  character  to  the  chord.  Please  think  very  deeply 
ui)on  this. 

ANSWER  TO  gUMS'lTON  27,  Key.  p.  2(3. 

.\  Discord  is  simply  a  disagreeable  sound;  a  Disso- 
nance means  something  unfinished,  or  incomplete,  or  un- 
rest ful. 


50  Graded   Lessons   in    Harmony 

A  dissonance  may  be  very  beautiful  in  effect,  for  exam- 
ple :  The  chord  of  the  Dominant  seventh  is  a  dissonant 
chord  and  yet  it  is  a  favorite  chord;  it  is  dissonant  be- 
cause it  is  unrest ful  or  needs  something  to  follow  to  com- 
plete the  thought.  Dissonance  is  the  proper  technical 
term  to  use,  not  discord. 

COLLATERAL    READING. 

58.  INVERSION  OF  INTERVALS. 

(1)  Statement.  An  interval  is  inverted  by  changing 
the  relative  positions  of  the  two  notes;  the  upper  one 
being  lowered  one  or  more  octaves  till  it  stands  below  the 
other  note,  or,  the  lower  note  being  raised  till  it  stands 
higher  than  the  other;  e.g.,  C-F  by  inversion  will  become 
F-C;  D-F  becomes  F-D,  etc.  The  use  of  this  principle 
becomes  apparent  when  we  observe  that  the  different 
notes  of  a  chord  appear  in  various  order,  first  one  note 
and  then  another  being  highest  or  lowest. 

(2)  Exercise.  First  at  the  keyboard  and  then  in 
writing,  invert  the  following  intervals :  C-E,  B-F,  F-C, 
E-D,  D-B,  E-F,  G-B,  etc. 

(3)  Statement.  To  determine  the  interval  which  shall 
result  by  inversion,  subtract  the  number  of  the  interval 
from  9;  e.g.,  a  third  by  inversion  will  become  a  sixth, 
since  9 — 3=6. 

(4)  Exercises.  What  interval  will  result  by  inverting 
D-F?  Answer:  D-F  is  a  third,  and  the  inversion  will  be 
F-D,  a  sixth,  since  9 — 3=6.  Similarly,  describe  the  in- 
versions given  in  (2). 

(5)  Statement.  Complementary  Intervals.*  Any  in- 
terval and  its  inversion  taken  together  form  what  are 
called  comi)lementary  intervals,  or  intervals  necessary  to 
complete  the  octave.  Read  Key,  p.  21 :  "Complementary 
Intervals." 


*The  term  "CompleraeiUary  Interval"  is  in  a  way  only  another  expression 
of  the  word  "inversion."  Its  special  office,  however,  is  to  call  attention  to  the 
fact  that  the  two  intervals  (i.e.,  the  given  interval  and  its  inversion),  together 
always  extend  over  exactly  an  octave,  each  one  complementing  the  other  and 
rounding  out  the  octave. 

The  deeper  meaning  implied  is  that  the  whole  of  musir  taken  as  a  science 
is  in  a  sense  contained  within  the  octave.  It  is  a  little  difficult  to  make  this  point 
clear  in  words.  It  is  rather  something  which  is  gradually  absorbed  as  these 
various  principles  are  studied  in  their  relations  and  interrelations  with  each 
other. 


(ffdclcd    Lcs.soii.s    ill    Harmon  if  51 

(G)  Exercises.  What  is  the  iiucrval  complementary 
to  the  fourth?  Jo  the  seventh?  To  the  fifth?  To  the 
unison?  To  the  sixth?  To  the  third?  To  the  second? 
To  the  octave? 

(7)  Statement. 

By  inversion  Major   intervals   become   Minor. 

By  inversion  Minor  intervals  become  Major. 

By  inversion  Augmented  intervals  become  Diminished. 

By  inversion  Diminished  intervals  become  Augmented. 

By  inversion  Perfect  intervals  remain  Perfect. 

(8)  Observation.  In  the  foregoing  table  the  correla- 
tive or  complementary  quality  of  Major  and  Minor,  and 
of  Augmented  and  Diminished,  become  very  clear.  The 
importance  of  the  principle  will  be  noted  when  the  differ- 
ent chord  forms  (positions  and  inversions)  are  under  con- 
sideration, for  in  the  absence  of  these  complementary  or 
correlative  qualities  a  chord  would  often  completely 
change  its  character  by  inversion.  To  illustrate :  In  the 
chord  G-B-D-F  is  a  Diminished  fifth,  B-F.  In  the  inver- 
sion of  this  chord,  D-F-G-B,  the  same  letters,  B-F,  by 
inversion  become  F-B,  which  is  an  Augmented  fourth. 
Now,  if  Diminished  and  Augmented  intervals  were  not 
complementary  or  correlative,  the  character  of  the  chord 
would  necessarily  be  changed  by  the  inversion.  That  the 
character  is  not  changed  is  one  more  illustration  of  the 
perfect  working  of  Nature's  laws. 

(9)  Observation.  While  Major  and  Minor  are  cor- 
relative, as  are  also  Diminished  and  Augmented,  the  Per- 
fect intervals  remain  in  a  class  by  themselves.  This  is 
an  important  difference  between  Major  and  Perfect,  that 
while  Major  intervals  by  inversion  become  Minor,  the 
Perfect  intervals  remain  Perfect  when  inverted. 

(10)  Exercises.  Prove  experimentally  the  statement 
in  (7)  and  (9),  by  inverting  at  the  keyboard,  and  also 
in  writing,  various  Major,  ]Minor,  Augmented  and  Dimin- 
ished intervals. 


Graded    Lessons    in    Ilannoni/ 


LESSON    8. 

INTERVAl.S   (Cont.) 

Consonant  and  Dissonant  Intervals. 

;Motto — To  fully  understand  the  principle  here  yiieu  and 
its  application  as  shozvn  in  later  lessons,  us  to  come 
7Tr\'  near  the  Heart  of  Music,  and  to  see  the  zeork- 
ings  of  one  of  Nature's  great  Laii's. 

59.  STUDY.  Learii  thoroughly  §75  of  H.  S..  with  this 
reservation — that  it  is  not  important  to  know  which  are 
perfect  and  which  are  imperfect  consonances,  as  the  two 
are  treated  alike  in  Harmony.     Read  Key.  75  (b). 

EXERCISES. 

Turn  to  all  the  exercises  in  notation  in  tiiis  chapter, 
and  observe  each  interval,  giving  its  specific  name  and 
stating  whether  it  is  consonant  or  dissonant.  \\  rite  a 
few^  examples  from  among  them,  especially  the  more 
difficult. 

WRITTEN   EXERCISES. 

Write  the  series  of  consonant  intervals  from  the  note 
C  as  the  lower  tone.  Illustration  and  answer:  We  must 
remember  that  all  of  the  intervals  are  represented  as 
contained  within  the  octave,  so  that  if  we  take  a  given 
note,  for  example  C.  and  place  it  in  connection  with 
every  other  tone  of  the  octave,  we  will  have  all  the  inter- 
vals (all  of  the  different  kinds).  C-C  is  a  Perfect  uni- 
son; C-Ctf  is  an  Augmented  unison;  C-Db  is  a  Minor 
second,  etc.  (Note  that  some  of  the  intervals  are  ex- 
pressed in  two  different  ways,  as  C-Ci  and  C-Db.) 
(Observe  also  the  abbreviations  occasionally  used — Maj., 
]\Iin.,  Dim.  and  Aug.  for  Major,  Minor,  Diminished  and 
Augmented;  also   Pcrf.   for  Perfect.) 

With  this  cxi)lanation,  let  us  take  the  Xt)tc  C  in  con- 
nection with  every  other  (chromatic)  tone  of  the  octave 
i!i  tin-n.  and  select  those  intervals  which  according  to  §75 


( I  null  it    I.csxoii.s    in    II (irmoii  ji  $i 

n(    //.  .S.,  aic  consonaiil,   willi  llir    Idllowing   result:  C-C, 

IVtI'.    unison;   C-l'-b,    Min.    third;    C-IE,   :\Iai.    third;  C-F, 

I'erf.    fourth;   C-G,    Pert,   fifth;    C-Ab,    Min.    sixth;  L"-A, 
Alaj.  sixth;  and  C-C,  Perf.  octave. 

XoTK.  To  form  tlie  series  of  dissonaiU  intervals,  we  need 
only  to  take  the  reniainino  intervals  of  the  octave,  as  all 
internals  must  fall  under  one  of  titese  too  classes.  For 
example:  C-CS,  .^ur.  unison;  C-Db,  Min.  second;  C-D,  Maj. 
second:  C-Fif,  Aug.  fourth;  C-Gb,  Dim.  fifth;  C-At,  Aur. 
sixth:  C-Bb,  Min.  seventh:  C-B,  Maj.  seventh;  and  C-Cb. 
Dim.  octave,  are  all  dissonant  intervals.  Xow  proceed  with 
the    follinving-. 

CO.  WRPrTEX  EXERCISE. 

A\'rite,  as  shown  above,  first  the  consonant  and  then 
the  dissonant  intervals  from  the  following  notes:  d  ;  h" ; 
Kb;  E;  Ab ;  B;  Db ;  F*.  (Continue  from  other  notes 
until  facility  is  gained.) 

KEYBOARD  EXERCISES. 

Proceeding  as  above,  form  tlie  series  of  consonant 
intervals  and  then  the  series  of  dissonant  intervals,  from 
each  of  the  following  notes:  C;  I);  Bb  ;  A;  Gb  ;  GU  etc. 
1  f  possible,  use  the  metronome  in  forming  the  series  and 
note  the  speed  of  the  first  and  the  later  attempts. 

RI'.CITATION. 

Recite  the  series  of  consonant  and  dissonant  intervals 
as  above,  noting  the  speed  attained. 

Gl.  EAR-TRALXIXG. 

Continue  as  directed  in  previous  lessons;  try  particu- 
larly to  sing  them.  From  now  on  try  to  observe  from 
the  effect  which  are  consonant  and  which  dissonant.  Let 
a  friend  play  different  intervals  (write  out  a  promiscuous 
series  for  him  to  play,  if  necessary)  while  you  listen 
carefully  as  each  one  is  repeatedly  played,  and  decide 
as  to  its  specific  name,  which  will  of  course  determine 
its   consonance   or   dissonance. 

XoTE.  When  played  by  themselves  you  will  be  unable  to 
distinguish  between  certain  ifitcrvals  (for  example,  the  .'Vut;;. 
fifth  and  ]\Hn.  sixth,  or  the  Aug.  second  and  Min.  third, 
or  the  .Aug.  fourth  and  Dim.  fiftli).  for  the  sound  will  he 
identical,     ^'et    this  nex'er  makes  confusion   in   liearinH'  music, 


54  Clrudcd   Lessons    in    Hai-mont/ 

for  the  otlicr  tone  vr  tones  present  will  unfailingly  indicate 
which  is  intended.  This  is  like  interpreting  a  sentence  by  the 
context. 

G2.  QUESTIONS. 

Write  answers  to  questions  30-35,  Key,  p.  2G. 

63.  ANSWERS   TO    QUESTIONS  30-32,   34-35,   p.   2G, 
Key. 

ANSWER  TO  QUESTION  30. 

Consonant  Intervals  in  a  Key. 

Perfect  Unisons.  Perfect  Fifths. 

Minor  Thirds.  Minor  Sixths. 

Major  Thirds.  Major  Sixths. 

Perfect   Fourths.  Perfect  Octaves. 

Dissonant  Intervals  in  a  Key. 

Aug.  Unisons. 
Dim.  Seconds 

(not  in  common  use). 
Min.   Seconds. 
Maj.  Seconds. 
Aug.  Seconds. 
Dim.   Thirds. 
Aug.  Thirds 

(not  in  common  use). 
Dim.  Fourths. 

Aug.  Fourths. 

ANSWER  TO  QUESTION  31. 

This  is  intended  to  bring  out  the  idea  that  all  chords 
must  be  classified  under  one  of  these  two  heads  (conso- 
nant or  dissonant)  and  treated  accordingly. 

It  will  simplify  matters  very  much  in  future  to  bear 
this  point  constantly  in  mind :  that  all  consonant  chords 
are  treated  according  to  certain  principles,  and  all  disso- 
nant chords  are  treated  according  to  entirely  different 
principles. 

ANSWER  TO  QUESTION  32. 

In  the  Major  scale  the  intervals  formed  by  the  Tonic 


Dim. 

Fifths. 

Aug. 

Fifths. 

Dim. 

Sixths  (seldom 

used 

Aug. 

Sixths. 

Dim. 

Sevenths. 

Min, 

Sevenths. 

Maj. 

Sevenths. 

Aug. 

Sevenths 

(not  in  common  use). 

Dim. 

Octaves. 

(traded    Lessons    in    Uannonij  55 

and  Third  .'ind  the  '["oiiic  and  Sixth  taken  ti)<;ellier  arc 
Major,  while  in  the  Minor  scale  these  intervals  are  Minor. 
Further,  to  change  a  Major  to  a  Minor  scale,  we  lower 
the  third  and  sixth  degrees  a  half-step.  Now  as  the  inter- 
vals of  a  Maj.  third  and  Major  sixth  are  changed  to 
Minor  in  the  same  way  as  the  Major  scales  are  changed 
to  Minor  scales,  the  relation  between  the  Major  scales 
with  their  Major  third  and  Major  sixth,  and  the  Minor 
scales  with  their  Minor  third  and  Minor  sixth  becomes 
apparent. 

ANSWER  TO  QUESTION  34. 

By  color  is  usually  meant  the  degree  of  cheerfulness, 
or  brightness,  upon  the  one  side ;  or  of  sadness,  etc.,  upon 
the  other  side.  You  will  find  as  you  go  on  in  the  study 
of  music,  a  close  comiection  between  Major  intervals 
and  the  brighter  compositions,  and  between  Minor  inter- 
vals and  Minor  compositions ;  but  you  must  not  think  that 
this  means  that  we  cannot  find  any  ]\Iinor  intervals  in  a 
liright  composition,  for  we  can. 

ANSWER  TO  QUESTION  35. 

As  we  trace  the  subject  further,  we  find  that  the  large 
intervals  in  the  motive  of  a  composition  (intervals  like  a 
fifth,  a  sixth,  or  an  octave)  tend  to  make  the  composi- 
tion more  robust,  rugged  and  aggressive  in  character; 
while  the  smaller  intervals  like  the  half-step,  or  a  second 
or  third,  tend  to  make  the  composition  quiet,  meditative 
or  sad.  It  is  particularly  interesting  to  study  the  motives 
in  Wagner's  operas  with  this  in  view. 

64.     SPECIAL  NOTE. 

Did  you  ever  observe  that  it  is  tlie  fifth  of  a  chord  which 
is  most  important  in  determining  whether  it  is  to  be  Aug- 
mented or  Diminished,  while  the  quality  of  Major  or  Minor 
depends  chiefly  upon  the  third?  To  illustrate,  let  us  take 
the  chord  C-E-G.  To  make  the  chord  Augmented,  raise  the 
fifth  (please  also  note  that  the  Major  third  must  be  asso- 
ciated with  the  Augmented  fifth  to  make  an  Augmented 
Triad;  or,  in  other  words,  the  extra  large  fifth  requires  a 
large  third  to  accompany  it).  Now  return  to  C-E-G  for  a 
fresh  start.  To  change  this  to  a  Minor  triad  the  third 
must  be  altered.  And  if  we  now  wish  to  change  this  Minor 
triad  to  a  Diminished  seventh  the  change  is  made  by  lower- 
ing  the   fifth.     So   tliat  whenever   Augmented   or    Diminislied 


56  (hddcd    Lessons    i)i    Ifarmo)!// 

is  mentioned  my  mind  at  once  goes  to  the  tifth  of  the  chord, 
while  if  Major  or  Minor  is  mentioned  my  mind  goes  at  once 
to  the  third.  This  becomes  very  simple  and  practical  if 
we  remember  at  the  same  time  that  the  extra  large  fifth 
requires  the  large  (Major)  third  wliile  the  Diminished  fiftli 
requires  the  small  (Minor)  third. 

It  may  be  noted,  in  a  broader  way  that  the  quality  of 
Major  or  ]\Iinor  either  in  chord,  interval,  scale  or  melody 
depends  most  directly  and  essentially  upon  the  -quality  of  the 
third  of  the  scale  (if  the  scale  or  melody  is  under  discus- 
sion), or  upon  tlie  third  of  the  chord  if  the  chord  or  interval 
is  under  discussion.  The  third  is  even  more  important  in 
this  connection  than  its  complement,  the  sixth,  as  is  illus- 
trated in  the  Melodic  ]\Iinor  scale,  which  has  a  Minor  third, 
while  the  sixth  is  not  lowered.  So  we  may  conclude  that 
it  is  not  the  second  or  seventh  or  any  other  interval  but  the 
third  (and  in  a  lesser  degree  the  sixth),  which  is  primarily 
the  source  of  the  Major  and  ]\rinor  modes. 

65.  DISSONANT  INTERVALS  THAT  SOUND  WELL. 

Students  often  ask  why  an  Augmented  second  or  an 
Augmented  fifth  is  called  a  dissonant  interval  when  the 
Minor  third  or  j\Iinor  sixth,  sounding  like  them,  are 
classed  as  consonant. 

This  might  be  called  a  "Grammatical"  or  "Theoretical" 
classification,  since  a  few  dissonant  intervals  do  sound  like 
consonances  when  taken  alone.  But  considered  with  the 
"context"  the  dissonance  is  usually  apparent.  For  exam- 
ple, C-GJ  sounds  consonant;  but  take  C-E-G  and  holding 
the  C  and  E,  change  G  to  GS,  when  the  dissonance  will  be 
extreme.  This  is  what  I  mean  by  "context."  But  this 
kind  of  illustration  does  not  alzi'ays  work.  For  example, 
the  Diminished  fourth  does  not  readily  yield  an  illustra- 
tion;  the  best  I  can  do  is:  Take  Ab-C-F,  the  C-F  being 
the  Perfect  fourth ;  now  flat  F,  and  you  have  a  clear 
dissonance.  But  if  you  take  A^  as  context,  the  resulting 
chord  sounds  like  an  ordinary  Minor  triad. 

Like  most  musicians,  you  have  possibly  thought  that 
a  dissonance  is  the  same  as  a  discord,  but  there  is  a 
marked  difference.  While  a  discord  is  an  unpleasant 
sound,  you  should  realize  that  "dissonance"  does  not 
necessarily  mean  the  bad  sound  you  have  always  thought, 
but  rather  an  interval  or  chord  requiring  some  other  to 
follow  to  give  repose;  and  you  will  aways  find  these 
.\ugmented  seconds,  etc.,  followed  by  consonances. 


(iradcd    Lcss(>}ifi    in    Ilontiont/  57 

COLLATEKAJ.    RKADING. 

G6.  DIFFERENCES   BETWEEN   MAJOR  AND  PER- 
FECT INTERVALS. 

(1)  Statement,  (a)  Perfect  intervals  have  no  Minor 
form.  That  those  Normal  intervals  which  have  no  Minor 
form  should  be  called  Perfect  seems  at  first  thought  illog- 
ical :  since  they  are  apparently  more  limited  than  the 
Major  intervals.  The  significance  of  the  term  Perfect  is 
found  largely  in  the  mathematical  relations  of  the  vibra- 
tion numbers  of  the  two  tones  of  a  Perfect  interval. 

(b)  Perfect  intervals  become  Diminished  by  being 
reduced  one  half-step,  whereas  a  Major  interval  requires 
two  such  reductions  to  become  Diminished.  (This  is 
merely  another  statement  of  (a),  though  it  has  special 
significance  in  practice  work.)  This  is  shown  by  the  sub- 
joined comparison  of  the  intervals: 

(1)    Augmented  (2)    Augmented 

ii"j"'  Perfect 

Mmor  ■' 

Diminished  Diminished 

(c)  Perfect  intervals,  when  inverted,  remain  Per- 
fect, or  Normal,  while  Major  intervals  by  inversion 
become  Minor;  i.e.,  not  Normal. 

(d)  Perfect  intervals  cannot  be  made  smaller  with- 
out destroying  their  quality  of  "consonance"  (see  (2)  be- 
low), while  the  consonant  Major  intervals  do  not  lose  this 
consonant  quality  when  made  Minor.  This  fact  has  a  most 
important  bearing  upon  the  structure  of  chords  as  illus- 
trated in  the  following:  Play  the  chord  C-E-G,  noting  the 
consonant  effect ;  then  change  G  to  Gb,  playing  the  other 
notes  as  before,  when  the  dissonant  character  of  the  chord 
with  the  altered  fifth  will  be  api)arent.  Note  that  C-G 
IS  a  Perfect  fifth,  which  is  consonant  (see  (2)  below), 
and  loses  its  consonant  character  when  made  smaller, 
C-Gb.  In  contrast  to  this,  we  will  change  the  Major 
interval  C-E,  chord  C-E-G.  Play  it  as  before,  noting  the 
consonant  quality ;  then  change  E  to  Eb,  playing  the  other 
notes  as  before.  As  this  last  form  (C-Eb-G)  is  conso- 
nant, it  is  clear  that  a  consonant  Major  interval  may  be 
made  smaller  without  destroying  its  quality,  or  classifica- 
tion,   as   described    in    the    following   sections;    while    the 


58 


Graded ,  Lessons    in   Jlarmnnij 


Perfect  iiUcr\als  might  well  be  called  "sensitive"  inter- 
vals, since  they  cannot  be  altered  in  any  manner  without 
altering  their  character.  (Note — This  section  should  be 
read  again  after  (2)-(3)  below.) 

INTERVALS— CONSONANT      AND      DISSONANT. 

In  the  preceding  sections  we  have  considered  the  sub- 
ject of  intervals,  the  general  names,  specific  names,  and 
the  measurement  and  comparison  of  intervals.  We  now 
have  to  consider  the  subject  from  a  new  point  of  view, 
namely,  the  qualities  of  consonance  and  dissonance. 

(2)  Statement.  Intervals  are  classed  according  to 
their  musical  effect,  as — 

(a)  Consonant,  meaning  those  intervals  upon 
which  it  is  agreeable  to  pause,  and  which  do  not  need  to 
be  followed  by  another  interval  to  produce  a  pleasant 
eft'ect ;  and 

(b)  Dissonant,  or  those  which  are  not  satisfactory 
to  dwell  upon,  or  to  use  in  the  final  chord  of  any  compo- 
sition. 

(c)  Consonances  are  further  divided  into  Perfect 
and  Imperfect  consonances,  with  reference  to  the  degree 
of  concord,  as  follows : 


Consonances.* 


Perfect 


All  Perfect  intervals,  viz. : 
Perfect  Prime  (or  Unison), 
Perfect  Octave, 
Perfect  Fourth, 
Perfect  Fifth, 


Imperfect : 


IMajor  Thirds  and  Sixths. 
Minor  Thirds  and  Sixths. 

f    Seconds  and  Sevenths,  together  with  all 

Augmented     and     Diminished     intervals; 

Dissonances.  •{     i.e.,  all   intervals   other  than   the   Perfect 

intervals   and    Major    and    Minor    Thirds 

and  Sixths. 

(3)  Exercises,  (a)  Form  and  describe  various  inter- 
vals as  consonant  or  dissonant.  Particularly,  form  illus- 
trations with  different  chords,  similar  to  that  shown  in 
( 1  )   above. 


Graded  Lessons    in    Ilnrmoni/  59 

(b)  Find-  and  describe  dissonant  intervals  in 
cbords  ov  i)rinted  music,  carrying  the  practice  into  tbe 
daily  musical  life. 

(4)  Statement.  Referring  to  the  statement  (sec 
Collateral  Reading.  Lesson  5,  [1]),  that  chords  are  com- 
posite, and  for  their  character  depend  upon  the  character 
of  their  constituent  intervals,  it  should  now  be  understood 
that  (1)  When  all  the  intervals  of  a  chord  are  consonant, 
that  chord  will  be  consonant;  and  (2)  When  even  one 
dissonant  interval  is  found  in  a  chord,  that  chord  will  be 
dissonant.  This  leads  to  the  division  of  chords  into  two 
great  classes:  (1)  independent,  or  consonant  chords, 
which  do  not  require  to  be  followed  by  another  chord, 
and  which  indicate  the  quality  of  repose  or  inaction ;  and 
(2)  dependent,  or  dissonant  chords,  which  must  be  fol- 
lowed by  a  consonant  chord  to  give  the  feeling  of  rest 
or  completion.  One  of  these  qualities  (consonance  or 
dissonance)  is  characteristic  of  every  chord  in  music, 
leading  logically  to  a  consideration  of  the  great  principle 
of  Resolution,  or  the  progression  of  dissonance  to  conso- 
nance in  successive  chords,  or  intervals.  Read  also  Key, 
:•■>   (c). 

G7.  QUESTIONS  ON  INTERVALS :  Key,  p.  23. 

ADDITIONAL  QUESTIONS:  Key.  p.  25. 

68.  DAILY  TECHNIQUE  DRILL  IN  THEORY. 

(Note.    All  illustrations  are  here  given  in  the  key  of  D.) 

(1)    (a)   Form  all  the  Perfect  intervals  from  the  key- 
note. 

(b)  Change   each    of   these    Perfect   intervals   to 

Augmented. 

(c)  Change    each   of   these   Perfect   intervals  to 

Diminished. 

Illustration :  D-D  is  a  Perfect  prime ;  D-G,  a  Perfect 
fourth ;  D-A,  a  Perfect  fifth,  and  D-D,  the  Perfect 
octave.  Changed  to  Augmented,  thev  will  be,  respec- 
tively: D-DJ;  D-G*;  D-A$  and  D-D*.  Changed  to  Di- 
minished, they  will  be,  respectively:  (there  is  no  Dimin- 
ished prime)  ;  D-Gb ;  D-Ab  and  D'-Db. 


60  (lidded    Lessons    in    flarninni/ 

(2)    (a)    Form  all  the  ^Nlajor  intervals   from  the  key- 
note. 
{h)   Change  these  to  Augmented. 

(c)  Change  these  to  Diminished. 

(d)  Change  these  to  INIinor. 

Illustration:  D-E  is  the  Major  second;  D-FS,  the  Ma- 
jor third;  D-B,  the  Major  sixth,  and  D-OJ,  the  Major 
seventh.  The  change  to  Augmented  gives,  respectively: 
\)-E':  D-Fx  (double-sharp);  D-B^  and  D-Cx.  The 
change  to  Diminished  gives:  D-Ebb  (double-flat);  D-Fb ; 
1)-Bbb;  D-Cb.  The  change  to  Minor  gives:  D-Eb ;  D-F ; 
D-Bb,  and  D-C. 


(traded    Lc.sxoiis    in    J Iiirmoiii/  61 

LESSON   9. 

TRIADS. 

The  Principle  of  Chord  Building. 

yUyno—All  chord  forms  groi^'  out  of  the  Triad.  There- 
fore, facility  in  forming  the  triads  is  indispensable  to 
later  success.     Be  thorough. 

69.  XOTi:. 

We  will  first  study  triads  in  general,  learning  how  to  form 
any  and  every  one,  afterward  associating  them  in  keys  and 
using  them. 

NoTK.  So  manv  are  unable  to  readily  "tliink"  triads  that 
we  dare  not  take  'ativtliing  for  granted.  Therefore  we  will 
first  take  the  simple  drill  which  has  lieen  found  most  helpful 
in  class  work,  particularly  with  children. 

The  "Alternate"  Letter  Principle. 

Whereas  a  scale  consists  of  consecutive  letters,  the 
elemental  principle  of  chord  forming  is  the  use  of  altek- 
K.VTK  letters.  Preliminary  to  the  regular  study  of  triads 
we  will  therefore  learn  to  think  quickly  of  the  letters  in- 
volved in  any  and  all  triads,  excluding  all  thought  of  the 
sharps  or  flats.  (Note.  This  point  is  much  like  the 
(lifference  between  the  general  and  the  specific  name  of 
intervals.)  To  illu-strate,  the  letters  used  in  the  triad  of 
D  are  I),  F  and  A.  Note  that  it  is  not  F*  but  F.  If  the 
Major  triad  were  ro(|uire(l  we  would  use  FS,  but  we  have 
not  yet  come  to  that. 

EXERCISES. 

Recite  the  entire  series  of  triad  kllcr  forms,  as  fol- 
lows: C-E-G;  D-F-A:  E-G-B ;  F-A-C;  G-B-D;  A-C-E ; 
B-D-F;  C.  (The  last  letter,  C,  is  included  for  the  rhyth- 
mic effect.)  Continue  to  recite  this  series  till  a  speed  of 
100  or  more  is  attained,  saying  a  whole  group  of  three 
letters  for  each  beat.  Also  reverse  the  order,  as  follows: 
C-E-G;  B-D-F;  A-C-E;  G-B-D;  F-A-C:  F-G-B  ;  D-F-A: 
C. 


62  (ircidcd   Lessons    in    Harmon i^ 

Another  form  of  the  exercise  is  to  recite  all  of  the 
letters  in  alternating  form,  thus :  C-E-G-B-D-F-A-C,  etc. : 
then  from  D,'  D-F-A-C-E-G-B-D,  etc. ;  then  from  E  ;  from 
F,  etc. 

XoTE.  This  alternating  order  of  letters  in  a  chord  is  never 
violated,  even  when  sharps  or  flats  are  introduced.  (Even  the 
inversions  of  the  chords  are  traced  back  to  this  fundamental 
form.) 

Remembering  this  principle,  we  are  less  hkely  to  name  the 
notes  of  a  chord  wrong  by  substituting  the  flat  of  one  letter 
for  the  sharp  of  another,  to  say,  for  example,  Gb  when  we 
mean  Ft,  as  might  easily  occur  if  we  first  touch  the  keys 
upon  the  piano  and  then  name  them  witliout  system.  Looking 
upon  the  piano  at  the  notes  B-DJf-Ftt,  we  could  not  say  if 
we  remember  this  principle  of  alternate  notes  that  the  triad 
of  B  is  formed  bv  the  notes,  B,  Eb  and  Gb,  but  by  B,  D-  and 
FS. 

It  is  most  important  that  this  principle  be  thoroughly  ap- 
plied, as  it  is  so  necessary  in  all  later  work.  Rkmembkr, 
that  although  we  may  add  sharps  or  flats  we  cannot  change 
the  letter  name  of  a  note  and  still  retain  the  original  name  of 
the  chord.  Now  a  question :  What  letters  are  required  to 
form  the  triad  of  Gb?  (Note.  Before  reading  further  please 
mentally  answer  the  question.)  The  usual  classroom  answer 
is  Gb,  Bb,  Db,  but  we  should  remember  that  flats  and. sharps 
have  nothing  to  do  with  the  letter,  and  the  true  answer 
is  G,  B  and^D. 

70.  EXERCISES. 

Name  the  letters  forming  the  triad  of  FS.  (Ans. :  F, 
A  and  C.  Do  not  be  confused  by  the  absence  of  the 
sharps.) 

Similarlv,  name  the  letters  used  in  forming  the  triads 
of  Ab  ;  of  Bb  ;  CS ;  G* ;  E5  ;  B».  Write  the  answers  to  the 
last  four. 

Chord  Structure  in  General. 

71.  STUDY:  //.  S.,  §91  (to  the  Exercises  only)  ;  Key.  01 : 
Collateral  Reading,  §75,  (l)-(3).  Advanced  students 
also  read  H.  S.,  §90. 

DRILL  upon  the  above.  In  the  triad  C-E-G,  which 
note  is  the  root,  and  which  the  third,  which  the  fifth  ? 
(.\ns. :  C  is  the  root,  F,  the  third,  and  G  the  fifth.) 
Similarlv  name  the  root,  third  and  fifth  of  each  of  the 
following  triads:   A-Cf-E;   FJ-A-C ;   B-D-F;   F-A-C. 


Graded   Lessons    iti    1 1  arm  on  if  63 

XoTK.  This  exercise,  thougli  absurdly  simple,  is  Riven  to 
establish  the  identity  of  the  three  elements  of  the  triad.  It 
will  soon  be  necessary  to  have  the  point  to  use. 

72.  THE  MATERIAL  OF  MUSIC;  OR,  THE  SCALE 
AS  THE  BASIS  OF  ALL  MUSIC. 

In  the  scale  are  contained  all  the  materials  from  which 
music  is  constructed.  In  the  single  tones  of  the  scale  are 
found  the  melody  or  the  chief  part  of  it,  since  the  Chro- 
matic passing  tones  appear  not  as  the  real  substance  of 
the  melody  but  are  like  unimportant  decorations.  By 
combining'the  scale  tones  into  chords  the  harmonic  struc- 
ture is  developed,  therefore  we  may  say  that  both  melody 
and  harmony  are  developed  from  the  scale.  lurther, 
following  the  principle  of  alternate  letters  and  choosing 
only  TONES  BELONGING  TO  THE  SCALE,  wc  may  build  a  triad 
upon  EACH  DEGREE  OF  THE  SCALE;  that  is,  WC  cau  use  each 
scale  tone  in  turn  as  the  root,  upon  which  to  build  a  triad 
by  adding  the  third  and  fifth  above,  as  shown  in  H.  S., 
Fig.  2.").  We  make  therefore  seven  different  chords,  one 
upon  each  degree  of  the  scale.  Note  that  these  seven  dif- 
ferent triads  are  all  in  the  key.  Do  not  think  that  the 
triad  upon  the  first  degree  is  more  truly  in  the  key  than 
the  triad  upon  any  other  degree.     Now — 

STUDY:  Collateral  Reading,  §75,  (7) -(8),  and  H.  S., 
§91  (the  Exercises),  and  §92. 

OBSERVE:  (1)  That  the  triads  upon  the  different 
scale  degrees  differ  in  their  sound;  and  (2),  that  they 
differ  in  the  kinds  of  thirds  and  fifths  contained.  This 
leads  to  the  consideration  of 

The  Specific  Forms  of  Triads — Major,  Minor, 
Diminished  and  Augmented. 

70.   STUDY:  H.  S.,  §9;j;  Collateral  Reading,  §75,  (5)  and 
(9)  ;  Key,  93. 

NoTK  1.  The  abbreviations  Maj.,  Min.,  Dim.  and  Aur.  will 
l>e  used  for  the  four  kind  of  triads. 

Note  2.  Tn  the  following  work  the  triads  are  not  supposed 
to  be  in  any  particular  key,  but  simply  formed  from  any  re- 
quired note'by  adding  the  proper  intervals. 


64  Graded    Lessons    in    Iliirnioni/ 

XoTK  3.  It  will  be  easier  to  reiiieniher  the  intervals  re- 
quired for  the  Dim.  and  Aug.  triads  if  we  note  that  the  "extra 
small"  (or  Dim.)  fifth  is  used  with  the  "small"  (or  Min.) 
third,  to  form  the  Dim.  triad,  while  the  "extra  large"  fifth 
and  the  "large"  third  work  together  to  firm  the  largest  form 
of  the  triad,  or  Aug.  triad. 

SPECIAL  DRILL. 

(a)  Why  is  C-E-Cl  a  j\Iaj.  triad?  (Ans.  for  illustra- 
tion: "Because  it  has  a  Maj.  third  and  Perf.  fifth. "") 
Why  is  C-Eb-G  a  Min,  triad?  Because  it  has  a  Min. 
third,  C-Eb,  and  a  Perf.  fifth,  C-G.  Why  is  B-D-F  a 
Dim.  triad?  Why  is  D-FJf-AS  an  Aug.  triad?  Why  is 
A-C-E  a  Min.  triad? 

(b)  Describe  the  triad  C-E-iit.  Ans.:  It  has  a  Maj. 
third,  C-E,  and  an  Aug.  fifth,  C-G*,  and  is  therefore  an 
Aug.  triad. 

Describe  similarly  D-F-Ab :  F#-A-CJf ;  F#-A-C ; 
Bb-D-F# ;  Bb-Db-Fb  ;  A-C-Eb  ;  AS-CS-E  ;  A-C»-E. 

(c)  Write  the  Maj.  triad  upon  each  of  the  following 
notes  :  D  :  Eb  ;  G  ;  C  ;  Ab  ;  F  ;  Db  ;  A  ;  F«  :  D*  ;  B  ;  G$  ;  E  ; 

cs. 

(d)  \\'rite  Min.  triads  upon  the  same  notes. 

(e)  Write  Dim.  and  Aug.  triads  upon  the  same  notes. 

KEYBOARD   EXERCISES. 

(1)  (a)   Repeat  (c),  (d),  (e)  at  the  keyboard. 

(b)  Form  the  triad  of  C  Maj.  Xext  change  it  to 
Aug.,  then  back  to  Maj.,  then  to  Min.,  then  to  Dim. 

(c)  Proceed  similarly  with  the  triad  on  Db,  giving 
it  the  four  forms  in  succession,  then  with  the  triad  of  D, 
and  continue  through  all  the  chromatic  tones  in  the  octave. 

(d)  Also  write  this  exercise  complete  and  note 
speed  attained  with  the  same  at  the  keyboard. 

(2)  Form  various  Aug.  and  Dim.  triads  icitlwitt  first 
giving  the  Maj.  form.     .\lso  7vntc  examples  of  the  same. 

74.  QUESTTOXS   1-ir,,   Key,  pp.  .-.O-.-,!. 

COLLATERAL    READING. 

75.  It  is  not  intended  to  go  into  the  formation,  i)ositions 
and  inversions  of  triads  and  common  chords,  as  the  sub- 
ject is  covered  in  many  text-books,  but  rather  to  take 
up    a    few    thoughts    relating   to   the    subject,   which    may 

iiiit    lie    fiitind    in    all    books. 


(Inulcd    Lexxons    in    IlarmDUij  65 

(  I  )  Statement.  A  chord,  in  the  general  sense  of  the 
term,  and  as  generally  used,  is  an  imitation  of  the  Great 
Chord  of  Nature,  as  shown  by  comparison  with  what  is 
known  as  the  "Harmonic  Series,"  or  "Overtones."  (Na- 
ture's Chord  is  illustrated  by  the  series  of  tones  produced 
from  a  keyless  brass  horn,  or  by  those  produced  by  a 
vibrating  string.)  The  chord  of  three  different  notes 
(the  triad)  has  its  counterpart  in  the  first  notes  of  the 
Harmonic  Series.  Being  so  closely  in  accordance  with 
Nature  would  seem  to  argue  strongly  in  favor  of  the 
claim  of  superiority  of  our  musical  system  as  compared 
with  other  systems,  such  as  the  Chinese. 

(2)  Chord  structure  in  general.  A  chord  is  formed 
by  adding  the  intervals  of  a  third  and  fifth;  or  a  third, 
fifth  and  seventh;  or  a  third,  fifth,  seventh  and  ninth 
to  any  note  which  is  taken  as  a  root.  In  other  words,  a 
chord'  is  composed  of  a  series  of  thirds  superimposed,  or 
placed  one  above  the  other. 

(3)  Parenthetically,  it  might  be  observed  that  where- 
as a  scale  is  formed  of  consecutive  letters,  a  chord  is 
formed  of  alternate  letters.  The  chord  of  three  different 
notes  is  called  a  Triad.  This  is  the  simjilest  and  original 
form  of  the  chord  principle,  or  harmonious  combination 
of  different  pitches.  (Note.  Two  tones  in  combination 
form  an  interval;  three  or  more  tones  form  a  chord.) 
When  one  note  of  the  triad  is  doubled  to  make  four-part 
harmony,  the  triad  becomes  a  common  chord.  When  a 
chord  is  composed  of  four  different  notes,  being  composed 
of  alternate  letters,  it  is  called  a  chord  of  the  seventh. 
Similarly,  by  a  process  of  adding  thirds,  a  chord  of  the 
ninth,  a  chord  of  the  eleventh,  or  a  chord  of  the  thir- 
teenth may  be  formed.  The  latter  chords,  however,  are 
not  in  very  general  use. 

(4)  Statement.  Chords  arc  conipositc,  being  made 
uj)  of  intervals.  The  character  of  a  chord  depends  upon 
the  character  of  the  intervals  contained.  (See  Collateral 
Reading,  §51,   [1]). 

(5)  Statement.  Specific  Names  of  Triads.  There 
are  four  kinds  of  triads — IMajor,  Minor,  Augmented  and 
Diminished.  They  are  named  from  the  most  characteris- 
tic interval  contained,  as  follows:  A  Major  triad  has  a 
Major  third  and  Perfect  fifth,  counting  from  the  root. 
A     Minor    triad    has    a    Minor    third    rind     Perfect     tlftli, 


66  Graded  Lessons    in   Harmoni/ 

counting  from  the  root.  A  Diminished  triad  has  a  Minor 
third  and  Diminished  fifth.  An  Augmented  triad  has  a 
Major  third  and  Augmented  fifth,  counting  from  the 
root.  (The  characteristic  intervals  in  each  of  the  four 
kinds  of  triads  is  here  in  italics.)  It  is  desired  that  the 
relation  between  the  chord  and  its  most  characteristic 
interval  should  be  clearly  seen,  as  it  has  a  most  important 
bearing  upon  the  whole  structure  and  practice  of  music. 

(6)  Exercises.  Form  examples  of  each  of  the  four 
kinds  of  triads  from  each  chromatic  note  of  the  octave. 
(Note.  This  exercise  is  most  valuable  when  taken  in  sys- 
tematic form  and  with  increasing  speed,  controlled  by  the 
metronome.) 

(7)  Statement.  To  be  in  the  key,  a  chord  must  be 
composed  exclusively  of  scale  notes.  If  even  one  note  is 
not  a  scale  note,  the  chord  cannot  be  said  to  be  strictly 
in  the  key. 

(8)  Statement.  The  INIaterial  of  Music.  A  chord, 
either  a  triad,  chord  of  the  seventh,  or  other  chord,  may 
be  formed  upon  each  degree  of  the  scale.  The  seven 
notes  of  the  scale  and  the  chords  built  upon  these  seven 
notes,  may  be  said  to  be  the  alphabet,  or  the  prime  ele- 
ments of  music,  which  are  combined  much  as  language 
is  formed  to  express  every  emotion  possible  to  human 
experience. 

(9)  Statement.  Of  the  triads  formed  upon  the  seven 
scale  notes,  there  are  three  kinds.  Major,  Minor  and 
Diminished,  found  in  the  INIajor  mode  (or  scale)  ;  and  all 
four  kinds  are  found  in  the  Minor  mode.  It  might,  at 
first  thought,  seem  strange  that  a  Minor  triad  should  form 
part  of  a  Major  key.  In  this,  as  well  as  in  other  respects, 
a  key  represents  a  family  which  is  composed  of  dissimilar 
elements. 

(10)  Exercises.  Form  a  triad  upon  each  degree  of 
several  IMajor  and  Minor  scales,  and  describe  each  triad 
in  turn. 

(11)  Note.  Positions,  Inversions,  Marking  Chords, 
Connecting  Chords,  Figuring  Chords.  It  is  suggested 
that  the  earnest  student  should  make  thorough  drill,  par- 
ticularly at  the  keyboard,  of  each  point  in  turn.  Detailed 
directions  may  be  found  in  H.  S.  In  general  it  should  be 
noted  that  it'  is  possible  to  place  the  different  notes  of 
tile  chord  in  au\  desired  order. 


Graded   Lesnoits    in    Ilarnioni/  Qf 


LESSON    10. 

TRIADS   (Cont.) 

jNIotto — Be  thorough  and  patient.  As  soon  as  a  nczv 
tlioiight  is  grasped  take  it  to  the  keyboard  and  use 
it;  compare  it  with  the  points  previously  gained — 
that  is.  co-ordinate  it — and  find  its  relations  to  the 
subject  as  a  zvhole.  Especially  here,  learn  by 
Doing.  "Do"  each  point  as  it  unfolds  to  your 
mind. 

ro.  SPECIAL  DIRECTIOXS. 

Read  zvith  a  hand  upon  the  keys,  and  follow  the  un- 
folding of  the  idea  by  having  the  hand  go  through  the 
chord  forms  described.  This  is  most  practical  and  helpful. 

The  four  kinds  of  triads,  Maj.,  Min.,  Dim.  and  Aug., 
continued  from  preceding  lesson.  You  are  supposed  to 
have  written  the  series  of  triads  required  in  the  Key- 
board Exercises.  Lesson  9,  §73,  where  we  take  the  triad 
of  C  Major,  change  it  to  Augmented,  back  to  Maj.;  to 
Min.;  to  Dim.,  and  then  progress  to  the  triad  of  Db  and 
go  through  the  same  process,  etc.  Below  are  given  the 
triads  in  their  proper  order,  for  comparison  with  the  one 
written  by  the  student. 

Fifths:    c;  ,Gi,G  ,G  ,Ci>  ;  A?.  A  ,\?A'?,  Ay?;  A  ,Ai?,A  ,A  ,  A'-> 

Thirds:  E  ,E  ,E  ,E!7,Eb  ;    F  ,F  ,F  ,FS,F[,  ;    Fii ,  Fi,  Fi^,  F  ,F 

Roots:    C  ,C  ,C  ,C  ,C  ;  D:7,D:>,D!>,Db,D;,   ;  D  ,D  ,D  ,D  ,D 

12     3     4    5         12     3     4      5  12     3     4  5 

Fifths:     H>,B  ,Bl,,B;,,By:>;   B  ,Bi,B  ,B  ,  B ,  ;  C  ,Ci;,C  ,C  ,C'7 

Thirds:  G  ,G  ,G  .Gl7,G!,  ;  G^,G^,Gi:,G  ,(;  ;  A  ,A' ,A  ,A'?,A'7 

Roots:     E>,Ei7,Eb,E[7,ES   ;  E  ,E  ,E  ,E  ,E  ;  F  ,F  ,F  ,F  ,F 

12     3     4     5         12     3      4     5  12     3     4     5 

Fifths:     C-:,Cx,C;:,C?i,C     ;  D  ,Ui:,D  ,D  ,D[>;  E>,E  ,Eb,El,,EbI^ 

Thirds:  A?:,AS,A#.A  ,A     ;  B  ,B  ,B  ,  B>  ,Bi,;  C  ,C  ,C  ,Cb,Cb 

Roots;     FS, F#, Fii,  Fi,  FS  ;  G  ,G  ,G  ,G  ,G   ;  Ab,  A^Ab.A^A:-. 

12     3     4     5  12     3     4  5  12     3     4     5 

Fifths:    E  ,Ett,E  ,E  ,K>  ;    F  ,F^,F  ,F     ,Fl,;   F?i, Fx,  F?,  F#, F  ;  G 

Thirds:  Q, Cit, Cii, C  ,C  ;  D  ,D  ,D  ,D-,  ,Dh;  Dii,D^,D^,D  ,D  ;  F 

Roots:    A  ,A  ,A  ,A  ,A  ;   Bs,  B',,  Bs.B'^  ,B.:   B  ,B  ,B  ,B  ,B  ;  (' 

12      3     4^'  1234=;         12^4^  1 


()S  (iradfil    Lc.<<.'<())is    in    Ilarrnovi/ 

W  KITTEX  EXERCISES. 

If  you  have  not  already  done  so,  or  if  incorrect  at  the 
previous  attempt,  write  the  above  in  notes,  on  the  treble 
staff.  Write  from  memory,  or  rather  from  understand- 
ing— not  by  copying. 

XoTE  that  the  roots  of  the  series  above  form  a  chromat- 
ically ascending-  series,  C,  Db,  D,  Kb.  etc.  Note  further  that 
Db  could  also  have  been  written  C*,  Eb  as  DJ,  etc.  In  the 
aliove  the  simpler  form  was  taken  in  each  case — the  one  re- 
quiring fewest  double-sharps  or  double-flats  in  the  triads.  But 
it  is  advisable  for  the  student  who  is  somewhat  advanced  to 
write  and  recite  the  above  series  first  with  tiie  "flat"  root  and 
then  with  tlie  "sharp"  root,  changing  it  enbarmonically.  (For 
definition  of  "enharmonic,"   see  H.  S.,  §§24,  78.) 

77.  KEYBOARD  EXERCISES. 

Play  the  foregoing  series  of  triads,  without  referring 
to  the  printed  or  written  copy.  This  will  not  be  difficult 
if  you  will  first  fix  the  series  in  mind:  Maj.,  Aug.,  Maj.. 
Mi'n.,  Dim.;  "progress"  (to  the  next  root)  and  note  also 
that  in  passing  from  one  form  to  the  next  in  order,  only 
one  note  is  changed. 

TWO  METHODS  OF  PRACTICIXG  TPTE  ABOVE. 

(a)  As  each  successive  form  is  struck,  say  "Maj., 
Aug.,  Maj.,  Mill..  Dim.."  naming  each  form  and  striving 
to  be  conscious  of  ( 1 )  its  sound,  (2)  its  feeling  under  the 
fingers.  (3)  its  variations  from  the  Normal  or  Major 
form,  and  (4)  of  its  appearance  on  the  printed  page,  or 
the  way  it  would  be  written. 

(b)  As  the  successive  forms  are  struck,  name  the 
single  note  which  is  altered  to  create  the  new  form  each 
time.  For  example,  playing  C-E-G,  say  "Major  C-E-G." 
Then  when  you  change  to  the  Aug.  form,  say  "GS"  as 
vou  play  the  Aug.  triad.  If  you  were  to  change  from  the 
Maj.  to' the  Min.  form,  you  would  .say  "Eb"  or  "Min.  Eb" 
as  the  ]\Iin.  triad  is  struck.  Then,  as  you  strike  the  next 
triad,  Db-F-Ab,  you  would  say  "Maj. 'Db-F-Ab."  Begin 
this  practice  slowly,  M.AI.  .50,  and  tzvo  beats  to  each  chord. 
Then,  as  facility  is  gained,  increase  to  a  ra])id  speed,  say 
120-100,  with  one  beat  to  each  triad. 

PRACTICE  THIS  EXERCISE  BOTH  ASCEXDTNG 

\XI)    OFSCEXDTXC,.      Xotc   that    in    descending,    when 


(jrcidcd    Lessoits    in    II(irmi)nif  69 

you  cliange  from  the  Dim.  form  uf  one  triad  to  the  Maj. 
form  of  the  next  one  below — e.g.,  from  C-Eb-Gb  to 
B-DJt-F+f,  only  one  note  is  really  changed,  the  upper  two 
being  enharmonically  altered.  Practice  it  also  with  the 
left  hand.  Continue  the  training  daily  for  from  one  to 
three  weeks,  putting  most  of  the  time  upon  the  weaker 
points. 

AXOTHER  ASCENDING  FORM  is  as  follows:  Maj., 
Min.,  Dim.,  Min.,  Maj.,  Aug.  "Progress,"  e.g.,  C-E-G, 
C-Eb-G,  C-Eb-Gb,  C-Eb-G,  C-E-G,  C-E-Gtf;  now  "pro- 
gress" to  Db-F-Ab,  and  continue  as  before.  Practice  this 
in  the  two  ways. 

XoTi;.  The  above  series  becomes  more  or  less  "mechani- 
cal" in  a  short  time,  and  does  not  call  upon  the  reasoning 
powers  sufficiently.  So  we  must  devise  a  training  to  fill  this 
requirement,  one  that  will  not  allow  the  fingers  or  mind  to 
reach  a  conclusion  without  direct  and  independent  thought. 
This  point  is  gained  by  taking  the  triads  in  such  a  series  as 
to  prevent  each  one  from  being  formed  from  the  preceding, 
but  on  the  contrary,  formed  directly  by  the  knowledge  of  the 
intervals  composing  it.  Therefore  you  should  now  review 
the  statements  in  //.  .S'.,  §93,  about  the  component  intervals  of 
each  kind  of  triad. 

78.  RECITATION. 

(a)  Recite  the  notes  of  the  triad  of  C  IMajor  (C-E-G). 
Then  pass  upward  a  whole-step  from  C  to  D,  and  recite 
the  notes  of  the  Major  triad  on  D.  Pass  upward  a  whole- 
step  again  and  recite  the  notes  of  the  Major  triad,  con- 
tinuing the  process  until  C  is  reached  an  octave  higher. 
Then  commence  upon  CS  (also  sometimes  calling  it  Db) 
and  proceed  as  before,  naming  the  notes  of  the  Major 
triad  in  each  case. 

(b)  Repeat  the  process,  but  this  time  naming  the  notes 
of  the  Minor  triad  each  time. 

(c)  Proceed  as  before,  but  naming  the  notes  of  the 
Aug.  triads.  Note  here  that  you  should  not  mentally  first 
form  the  Maj.  triad  and  then  change  it,  but  you  should  go 
straight  to  the  Aug.  form  and  name  each  note,  remember- 
ing that  a  Maj.  third  and  Aug.  fifth  from  the  given 
root — whatever  it  may  be — are  required. 

(d)  Name  similarly  the  Dim.  triads,  remembering  that 
the  Min.  third  and    Dim.  fifth   are  required — do  not  first 


70  Graded  Lessons   in   Harmony 

f(inn  the   >rai.  or  Alin.,  that  is,  if  you  are  able  to  do  it 
without  this  help. 

WRITE  three  examples  of  Maj.  triads,  three  of  Min., 
three  of  Aug.  and  three  of  Dim.  triads.  If  you  will  pro- 
ceed chromatically  upward  from  C  to  C,  writing  the  triad 
of  C  I^Iaj.,  then  of  CS  Min.,  D  Aug.,  Eb  Dim.,  E  Maj.,  etc., 
the  twelve  required  examples  will  use  every  chromatic 
note  of  the  octave. 

KEYBOARD  EXERCISES. 

Repeat  the  foregoing  exercises  in  recitation  at  the  key- 
board, using  the  metronome,  and  reporting  accurately 
upon  the  speed  attained.  Do  not  try  to  go  through 
the  whole  of  the  above  in  one  day.  Rather,  use  it  as  a 
drill  to  be  carried  from  ten  to  twenty-five  days,  till  facility 
is  gained. 

79.  WRITTEN   EXERCISES. 

This  is  a  test  for  speed  and  accuracy.  Write  out  in 
capital  letters  the  notes  constituting  the  following  triads, 
timing  yourself  accurately  by  the  watch,  writing  plainly 
and  making  no  corrections,  not  even  to  add  a  sharp  or 
flat.  (You  may  afterward  place  a  ring  around  any  wrong 
notes  and  write  the  correction  outside  to  show  that  you 
understand.)  X'ote  the  time  required  for  the  whole  exer- 
cise— not  for  each  triad.  You  may  do  this  exercise  once 
as  soon  as  you  see  this,  and  then  again  when  the  lesson 
is  mastered,  to  note  the  progress. 

The  Test.  Write  the  notes  of  the  following  triads: 
B  Min.,  FS  Maj.,  C«  Aug.,  A  Dim.,  G  Aug.,  D  Aug.,  Gb 
Min.,  CJf  Dim.,  Ab  Dim.,  B  Aug.,  G?  Min.,  D«  IMaj..  Gb 
Dim.,  Db  Min.,  Di  Maj.  Remember,  no  corrections 
except  with  rings. 

KEYBOARD  EXERCISES. 

Play  the  preceding  triads,  noting  the  metronome  speed 
attained  upon  the  first  attempt  and  also  the  last.  Do  not 
forget  to  use  the  left  hand  part  of  the  time  upon  all  exer- 
cises. 

BO.  \'ARIETY  OF  DRILL. 

As  the  studv  of  the  formation  of  triads  in  tlu-ir   four 


(Irtidcd    T.i'ss(>>is    in    [[(irrnoiii/  71 

forms  is  to  be  continued  till  facility  is  gained,  it  is  well 
accomplished  by  changing  the  order  of  the  roots;  e.g., 
instead  of  taking  a  series  whose  roots  are  a  whole-step 
apart,  we  may  pass  upward  (or  downward)  a  Minor  third 
for  the  following  triad,  and  continue  to  pass  upward  (or 
downward)  a  Minor  third  each  time.  Then  similarly  we 
can  progress  a  Major  third  each  time,  or  by  any  desired 
skip  or  combination  of  skips.  One  of  the  most  useful 
skips  is  that  of  the  Perfect  fifth,  either  upward  or  down- 
ward. This  develops  knowledge  which  will  presently  be 
useful  in  another  way. 

KEYBOARD  DRILL. 

(a)  Following  the  above  suggestion,  form  a  series  of 
Major  triads,  using  one  or  more  of  the  suggested  ways 
and  note  the  speed  attained.  In  every  case  include  the 
progressions  of  the  Perfect  fifth  up  and  down. 

(b)  Form  a  similar  series  with  ]\Iinor  triads,  choosing 
a  different  progression. 

(c)  Form  a  similar  series  with  Diminished  triads. 

(d)  Form  a  series  with  Augmented  triads. 

WRITTEN  EXERCISES. 

Write  out  the  series  with  Augmented  triads,  progress- 
ing by  the  Perfect  fifths  upward,  then  by  Perfect  fifths 
downward. 

RECITATION. 

Recite  the  series  of  Diminished  triads,  progressing  by 
Perfect  fifths  upward  and  then  downward. 

Special  Note.  If  difficulty  is  experienced  with  the  forma- 
tion of  the  different  kinds  of  triads,  the  drill  must  be  con- 
tinued daily  for  some  time.  Do  not  expect  facility  simply 
by  understanding  them.  You  must  think  and  (/o  them  many 
times  before  the  mind  and  fingers  will  work  quickly.  And, 
further,  do  not  discontinue  this  drill  as  soon  as  the  next 
subject  is  undertaken,  but  return  frequently  to  this  portion 
for  a  review  and  drill. 

81.  EAR-TRAINIXG. 

To  ask  at  this  point  that  ear-training  be  carried  on 
from  the  beginning  of  the  studv  of  triads  is  nearly  like 


72  (irddcd   I.cssotis    in    Ifa rmoii  1/ 

the  postscript  of  Pat's  letter:  "If  ycz  don't  receive  tiiis 
yez  may  know  thot  I'm  well."  Yet  it  is  desired  in  connec- 
tion with  the  daily  study  in  each  and  every  day's  practice. 
It  is  especially  desired  that  this  be  done  to  make  each  fact 
and  principle  more  tangible  and  real,  and  that  the  ear  as 
well  as  the  eye  and  the  understanding-  may  be  called  into 
activity. 

82.  gUESTIOXS   17-2S,  Key.  pp.   r.l-.".2. 
S3.  ABOUT  THE  TERM  POSITIOX. 

"Position"  does  not  relate  to  the  order  of  the  notes 
in  the  chord,  but  it  relates  to  the  highest  note  only,  or 
Soprano,  and  not  to  any  other  note,  or  to  any  order  of 
notes.  The  above  statement  is  made  as  strong  as  possible 
to  ward  off  any  possible  misunderstanding,  for  pupils  are 
very  frequently  confused  about  this  for  some  little  time. 

When  a  triad  is  taken  with  one  hand,  changing  the 
position  does  naturally  bring  about  an  apparent  change  in 
the  order  of  the  notes,  but  this  change  in  the  order  of  the 
inner  notes  has  nothing  to  do  with  "position,"'  as  will  be 
seen  if  you  use  two  hands  and  spread  the  chord  out  over 
three  octaves,  when  you  will  see  that  the  order  of  the 
loiver  three  parts  may  be  freely  changed  without  affecting 
the  position. 

It  must  be  clearly  tuiderstood,  then,  that  position  re- 
lates to  one  tone  only  and  that  the  highest  in  the  chord. 
Read  H.  S..  !)() ;  also'A'n'.  nr.. 

84.  EAR-TRAIXIXG. 

(a)  Strike  the  triad  of  C  Major  upon  the  piano;  then 
listen  intently,  striving  to  hear  the  individual  tones  con- 
stituting the  chord,  but  not  striking  them  individually; 
try  to  sing  the  third  and  fifth  (the  top  note  is  always 
the  easiest  one).  Xow  strike  other  triads  and  try  to 
sing  the  tones  in  turn — to  commence  with  the  third  is  to 
show  a  good  ear. 

(b)  .Similarly  sound  Minor  triads  and  try  to  sing  their 
tones. 

(c)  Similarly  sound  Diminished  triads  and  try  to  sing 
their  tones. 

(d)  Similarly  sound  Augmented  triads  and  try  to  sing 
their  tones. 


(Iradcd    Lessons    in    Harmon i/  73 

XoTE.  These  exercises  will  help  y<>u  to  listen  with  con- 
centration and  intelligence  to  the  different  kinds  of  triads,  and 
will  help  you  to  recognize  thein  when  pla^-ed.  It  is  less  impor- 
tant that  you  succeed  with  those  exercises  than  that  you  make 
the  attempt,  and  so  come  to  listen  more  intently,  and  that  yon 
learn  how  to  listen. 

(e)  Plav  different  kinds  of  triads  in  different  parts  of 
the  keyboard,  noting  the  dift'erent  color  of  the  different 
kinds  of  triads,  and  also  how  the  same  kind  of  a  triad 
gives  a  different  effect  in  dift'erent  pitches,  which  makes 
the  subject  more  difticult. 

Bv  -color"  is  meant  that  a  Major  triad  gives  the  eft'ect 
of  brightness  and  satisfaction,  a  Minor  triad  of  sadness 
or  darkness,  a  Diminished  triad  of  dissonance  or  com- 
pression (the  notes  are  pressed  together),  and  an  Aug- 
mented triad  of  most  violent  dissonance,  together  wdth 
the  effect  of  expanding,  tearing  apart  or  openness.  Ob- 
serve that  both  Major  and  Minor  triads  are  consonant, 
while  Augmented  and  Diminished  are  both  dissonant  but 
quite  opposite  in  character. 

(f)  While  a  second  person  plays  the  various  triads 
upon  the  piano,  write  out  the  series  given  in  Lesson  10. 
§76.  If  necessary,  you  may  decide  as  to  the  character  of 
each  one  as  it  is  repeatedly  played. 

XoTi-.  If  a  second  person  is  not  available,  then  play  these 
different  kinds  of  triads,  with  intensely  concentrated  thought 
and  attention,  striving  to  hear  and  feel  the  qualities  or  colors  as 
described.  After  reaching  this  point  we  sliould  take  every 
opportunity  of  recognizing  the  various  kinds  of  triads  when 
listening  to  music.  Sucli  careful  listening  to  music  is  really 
the  beginning  of  self-production  of  musical  thoughts.  And 
now  w^e  come  to  the  more  difficult  Ear-iraininy  Exercises. 
which  will  not  be  done  by  more  tlian  a  quarter  of  the  students 
at  the  first  attempt,  and  by  not  more  than  one-half  after  many 
attempts— yet  the  attempt  is  zi'orth  ivhile.  even  if  you  fad. 

(g)  Sound  the  note  C  as  a  root,  and  while  holding  this 
note,  sing  in  succession  the  root,  third  and  fifth  of  the 
Major  triad.  Do  not  help  yourself  by  sounding  the  other 
tones  till  after  the  voice  has  taken  the  tone  and  then  only 
to  prove  the  result.  Repeat  with  other  notes  which  lie 
in  the  range  of  the  voice. 

(h)  Proceed  similarly  with  the  Min.  triads, 
(i)  Proceed  similarly  with  the  Dim.  triads, 
(j)    Proceed  similarly  with  the  Aug.  triads. 


74  Graded   Lessons   in   Harmony 

Do  not  hesitate  to  carry  on  the  above  exercises  for 
three  months  or  even  a  year,  for  they  are  potent  influ- 
ences in  developing  true  musicianship,  whether  you  ever 
succeed  or  not.     Do  not  worry  about  that  part. 

If  you  do  not  readily  succeed  with  the  above,  a  com- 
promise may  be  made  or  a  preliminary  training  secured, 
if  a  second  person  will  play  the  various  triads  in  "broken" 
form  while  the  student  endeavors  to  decide  the  nature  of 
the  triad  from  hearing  it  in  the  broken  form.  In  this 
way  the  ear  becomes  accustomed  to  hearing  the  melodic 
side  of  chord  building,  which  is  recognized  by  but  few. 


Graded    T.essoiis    in    Tltnttunii/ 


LESSON  11. 

TRIADS  (Cont.) 

85.  IMPROVISATION. 

This  is  one  of  the  most  important  lines  of  work  pos- 
sible to  the  Theory  student,  and  should  form  a  part  of 
every  day's  practice  to  the  end  of  the  course.  True 
familiarity  with  the  material  of  music  can  only  be  at- 
tained by  using,  at  the  keyboard,  each  new  element  as  it 
is  studied,  adding  to  our  working  material  item  by  item, 
until  we  can  use  all  the  ordinary  chords  freely  and  almost 
unconsciously,  to  express  musical  ideas.  The  common 
fault  with  efforts  in  this  line  is  that  they  do  not  begin  at 
the  beginning,  but  attempt  too  many  things  at  once  to 
succeed. 

As  a  child  commences  his  use  of  language  with  single 
words  of  the  simplest  character,  so  will  we  first  use  single, 
disconnected  chords  in  the  simplest  form  without  gram- 
matical significance.  But  this  simple  work  can  be  in- 
vested with  real  charm,  and  teachers  will  find  it  of  the 
greatest  advantage  to  use  the  following  exercises  with  all 
piano  pupils,  children  or  adults.  For  the  children  the 
original  forms  of  the  exercise  were  called  the  "Bounding" 
and  the  "Rocking"  chords,  the  reason  of  which  names 
will  be  apparent  later. 

"Bounding"  and  "Rocking"  Chords. 

The  term  "Bounding"'  chord,  as  here  used,  simply  de- 
notes the  repetition  of  the  chord  in  a  higher  octave. 
There  are  various  ways  of  performing  this  chord,  one 
which  is  shown  in  Fig.  2  below.  (Note — The  illustra- 
tion shows  the  chord  in  only  one  key,  but  it  will  be  played 
by  the  student  in  all  keys  to  gain  facility,  for  which  it  is 
one  of  the  most  important  means  yet  devised.) 

A  "Rocking"  chord  is  simply  a  form  of  the  "broken" 
chord  as  shown  in  Fig.  3. 

KEYBOARD  EXERCISES. 

(a)   Following     the     illustrations     in     Fig.     2,     form 


76  (irtidcd    T.cssons    in    J] nrinnn ji 

"Bounding"  chords  from  all  the  Major  triads,  progressing 
upward  by  half-steps. 

(h)  P'orm  a  similar  series,  progressing  downward  by 
half-steps.  As  soon  as  it  is  fairly  familiar,  work  with  the 
metronome,  repeating  the  more  difficult  ones  as  many 
times  as  may  be  necessary,  and  give  a  report  of  the  speed 
which  can  be  attained,  playing  in  quarter  and  half-notes 
as  indicated  in  the  illustration,  one  beat  to  each  quarter. 

(c)  Form  a  similar  series,  but  progressing  by  skips 
of  a  Perfect  fifth  each  time. 

(d)  Form  a  similar  series,  progressing  downward  by 
a  skip  of  a  Perfect  fifth. 

WRITTEN  EXERCISES. 

Write  examples  of  "Bounding"  and  "Rocking"  chords 
in  at  least  four  keys.  Be  sure  to  write  them  exactly  as 
you  play  them,  for  the  correctness  of  the  keyboard  work 
can  only  be  judged  in  this  way.  Write  also  all  those 
chords  about  which  vou  mav  be  in  doubt. 


"  RorXDIXCx  ("HORnS." 


Fig.  2.  J  -^ 


— 6> ©>- 


:t: 


Fed. 


Repeat  in  all  keys. 


Fig.  3. 


"ROCKING  CHORDS." 


=*=f: 


'^Et^ 


'^^^^^ 


Fed. 


#  Fed. 


#  Fed. 


Repeat  in  all  keys. 


Graded    Lr.i.son.s    in    1 1  a  niioii  1/  77 

CX).\NECTR).\  UF  "iK)L  NUING  CliORDS." 


Fig.  4.^'^     •:  ^  J^ 

-  -A-^<—W-^^ — i-='-i — 1- 

-^-# — »-^-oi — m — 
-•-     •-  -0- 


/vrf. 


-S- 


# 


*  p^i/. 


-n 


1k9—<St ^- 


1/ 


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^=«u- 


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:^ 


-^2-: 


'N   -5-1  > 


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r 


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red. 
1 


78  Graded  Lessons    in   Ilannoni) 


LESSON  12. 

TRIADS:  THEIR  POSITIONS   AND 

INVERSIONS. 

86.  XoTi;.  Before  taking  up  the  study  of  position,  the  student 
should  understand  the  terms,  Principal  and  Secondary  Triads 
and  Doubling. 

Principal  and  Secondary  Triads. 

STUDY  H.  S.,  §94. 

WRITTEN  EXERCISES. 

Write  the  seven  triads  in  the  scale  of  D  ]\Iajor; 
describe  each  one  as  required  under  the  head  of  Exercises, 
H.  S.,  §94. 

Doubling, 

87.  STUDY  //.  5".,  §95. 

WRITTEN  EXERCISES. 

Write  the  chord  of  G  Major  in  four  parts  in  several 
different  ways ;  that  is,  doubling  different  notes,  indica- 
ting which  forms  are  best  and  which  are  poorest. 

Position. 

88.  STUDY  H.  S.,  §90;  also  Key.  W. 
WRITTEN  EXERCISES  :  H.  S.,  §9(;. 

KEYBOARD  EXERCISES. 

I'ollowing  H.  S..  Fig.  27,  as  a  jiattern,  play  every 
IMajor  and  IMinor  triad  in  its  three  positions. 

XoTF..  Instead  of  studying  part-writing  at  this  point,  the 
student  will  skip  for  the  moment  from  //.  S.,  §97  to  §125.  We 
will  do  this  for  the  purpose  of  studying  the  construction  of 
chords  more  tliorouglily  l)efnrc  taking  up  tlic  study  of  part- 
writing. 


Graded   Lessons    in    Uurmoni/  79 

89.  EAR-TRAINING. 

In  the  second  lesson,  §!(),  the  individual  qualities  of 
the  scale  tones  were  shown.  The  student  will  now  be 
able  to  use  this  knowledge  in  determining  the  different 
positions  of  a  chord.  By  listening  intently  to  the  upper 
tones,  the  quality  of  either  rest  or  incompleteness  may 
be  heard.  By  singing  the  upper  tone  when  playing  the 
three  positions  in  succession  the  quality  may  become  more 
marked.  The  student  should,  however,  be  warned  that 
this  is  not  an  easy  matter  for  a  large  proportion  of  musi- 
cians, and  it  may' require  six  months  or  longer  to  become 
proficient  in  this' line.  Those  gifted  with  accurate  hearing 
may  be  able  to  distinguish  almost  at  the  first  attempt.  It 
would  be  well  in  this  exercise  if  a  friend  could  play  chords 
in  different  positions. 

To  "Hear"  or  Sing  Any  Required  Tone  of  a  Chord 
When  All  Are  Played  Together — Not  Broken. 

To  successfully  distinguish  the  various  chords  in  their 
different  positions  and  inversions,  it  is  essential  that  the 
student  should  first  be  able  to  sing  at  will  any  one  of  the 
tones  of  a  common  chord,  picking  out  any  tone  from  the 
mass  as  the  chord  is  sounded  with  all  its  tones  together. 
For  some  persons  this  is  very  easy,  for  others,  extremely 
difficult.  Therefore,  each  student  is  required  to  report 
specifically  upon  this  point,  and  if  any  particular  difficulty 
is  found, 'do  not  try  to  go  on  with  the  next  exercise  till 
after  several  weeks,  or  even  months,  of  training  in  this 
line.  The  above  exercise  is  one  that  the  student  can  do 
with  considerable  success  by  himself,  striking  any  chord 
upon  the  piano  (not  forgetting  to  try  the  different  posi- 
tions and  inversions),  and  especially  striking  all  the  tones 
together  and  then  trying  to  sing  the  different  tones  of  the 
chord  at  will,  attempting  particularly  the  inner  tones, 
which  are  more  difficult  than  the  highest  or  lowest  tones 
of  the  chord. 

Positions. 

The  student  will  remember  that  in  the  second  lesson, 
§10,  the  individual  qualities  of  the  scale  tones  were  dis- 
cussed, the  Tonic  being  firm,  the  Third  calm  and  the 
Fifth  bright.  By  listening  carefully,  you  will  be  able  to  tell 


80  iirddid    Lessons    in    II iirtiioii  i/ 

which  tone  of  a  chord  is  highest,  that  is,  to  (Iclerniiiif 
the  position  of  the  chord.  Other  helps  may  occur  to  you, 
as  for  example,  to  try  to  think  how  far  it  is  down  or  up 
to  Doh,  or  the  point  of  rest ;  or  to  notice  as  you  sing  the 
various  notes  upward  or  downward,  what  the  intervals 
are.  For  illustrations,  when  the  fifth  of  a  chord  is  high- 
est, it  will  be  a  Minor  third  above  the  next  note  below ; 
or  if  the  octave  is  highest,  it  will  be  a  fourth  above  the 
next  highest  note,  and  if  you  were  to  add  (experimen- 
tally) another  note  above,  it  would  be  a  Alajor  third. 
Some  people  with  unusually  keen  musical  hearing  can  dis- 
tinguish the  positions  of  a  chord  without  reasoning,  but 
this  is  not  expected  of  the  student.  It  is  a  faculty  to  be 
gained  by  hard  work  and  plenty  of  it. 

Inversions. 

The  principles  discussed  above  will  apply  equally  to 
the  lowest  tone  in  a  chord,  and  the  student  should  give 
especial  attention  to  the  lowest  as  well  as  the  highest  note. 
When  these  two  tones  become  clear  in  the  mind  it  is 
comparatively  easy  to  decide  upon  the  intervening  tones, 
which  will  result  in  a  real  knowledge  of  the  complete 
chord.  Remember  that  this  work  cannot  be  accomplished 
in  a  short  time,  and  those  not  gifted  with  especially  good 
hearing  should  frequently  review  the  simplest  exercises  of 
the  descending  tones  of  the  scale  and  the  simplest  inter- 
vals, for  upon  this  foundation  the  ability  to  hear  as  well 
as  the  ability  to  construct  chords  is  developed. 

90.  OUb:.STIOXS  2'.»-:;i.  Key.  p.  :e2. 

91.  XOTl'    ABOUT  MIXIXG  POSITIONS   AXi:)   IXVI'.R- 

SIOXS. 

Althuugh  students  make  the  slatcnicnl  and  beli<j\c  il,  tliat 
position  refers  to  Soprano  and  inversion  relates  to  the  Bass, 
yet  when  the  position  is  allowed  to  change  with  tlie  changing 
inversion,  one  is  forced  to  suspect  that  in  the  subconscious 
mind  of  the  student  the  position  is  affected  by  the  inversion. 
This  should  not  be  and  the  student  should  give  careful  atten- 
tion to  this  point,  for  it  will  be  met,  either  in  his  own  study 
or  in  his  experience  as  a  ti-achcr:  think  it  out  carefully. 

In  teaching  and  drilling  the  inversions,  you  will  find  a 
tendency  on  the  part  of  your  pupils  to  shift  the  position  every 
time   tlic    i-ass  is  cli.'Uiucil.  letting  flu'   Soprruio  gcj  up  as   fast 


Graded    Lessons    in    Harmon  1/  81 

as  the  Bass  does.  This  will  give  the  wrong  impression,  for 
we  wish  to  confine  the  thought  to  the  change  in  the  Bass. 
Therefore,  always  require  pupils  to  keep  the  same  position 
as  far  as  possible  throughout  the  different  inversions;  or 
rather,  ask  them  to  play  through  the  different  inversions, 
first  retaining  one  position,  then  repeat  it  with  a  changed 
position  and  so  on  till  each  position  has  been  used  for  all  the 
inversions. 


82  Graded   Leaauns    in   Ilurmonif 


LESSON  13. 

INVERSION  OF  TRIADS. 

92.  STUDY  H.  S.,  §12.5.     Observe  particularly  the  foot- 
note. 

WRITTEN  EXERCISES:  H.  S.,  §125. 

KEYBOARD  EXERCISES. 

Using  two  hands,  play  every  Major  and  Minor  chord 
in  its  direct  form  and  two  inversions,  as  shown  in  Fig.  38, 
H.  S.     Note  the  speed  attained. 

XoTE  1.  It  should  be  observed  that  the  whole  substance  of 
"positions"  and  "inversions"  resolves  itself  into  this:  That 
as  the  tones  of  an  interval  may  be  inverted  without  destroying 
its  character,  so  the  tones  of  a  chord  may  be  inverted  or  used 
in  ditferent  orders  without  destroying  the  character  of  the 
chord;  and  that  the  relationships  of  the  different  tones  of  a 
chord  to  the  root  are  not  essentially  altered,  regardless  of  the 
order  in  which  the  tones  appear.  The  student  should  now 
review  the  lessons  on  the  inversions  of  intervals  and  trace  out 
the  logical  connection  between  the  intervals  and  chords, 
remembering  particularly  that  chords  are  composed  of  inter- 
vals and  the  intervals  give  character  to  the  chords.  There- 
fore, the  principles  which  govern  the  relationships  of  the  tones 
of  an  interval  will  continue  in  force  when  intervals  are 
grouped  into  chords. 

Note  2.  The  student  should  further  observe  that  in  study- 
ing positions,  inversions  and  doubling,  we  have  but  three 
tones  to  consider, — the  root,  third  and  fifth  which  we 
studied  in  our  first  lesson  on  triads.  These  three  tones,  root, 
third  and  fifth,  may  occur  in  any  desired  order,  but  the  rela- 
tionships of  the  tones  one  to  the  other  remain  unchanged 
throughout  these  many  different  forms. 

If  these  points  are  held  carefully  in  mind  the  subject  will 
take  a  far  simpler  form  in  the  mind  than  is  otherwise  possible. 

93.  FIGURIXG  TRIADS. 

Note.  Very  frequently  students  become  contused  when 
stndyinu  the  figuring  of  triads  liccausc  they  forget  that  there 


(irddcd    Lessons    in    H a rnion  1/  83 

arc  hill  three  dilTerenl  notes  and  that  these  notes  are 
not  chanijed  altliouj^Ii  the  chord  appears  to  he  (juitc  different. 
l'"nrtlier,  let  us  renieniher  that  fi.uurinj^  triads  is  simply 
a  process  of  showing  whether  the  root,  third  or  fifth  is  in 
the  bass. 

STUDY  H.  S.,  §§127-128,  also  §130. 

WRITTEN  EXERCISES:  H.  S.,  §128.  (Sec  Key, 
128.) 

To  Find  the  Root  of  An  Inverted  Triad. 

9i.  STUDY  H.  S.,  §129. 

WRITTEN  EXERCISES:  //.  S.,  §129.  (See  Key, 
129.) 

DRILL. 

Turn  to  various  simple  hymn  tunes  and  find  the  roots 
of  the  inverted  chords,  and  write  out  the  chords  (contain- 
ing not  more  than  three  different  letters)  the  roots  of 
which  you  may  be  unable  to  find. 

Read  H.  S.,  §131,  but  do  not  study  it,  as  you  will  come 
to  it  again  later  on  in  connection  with  part-writing. 

Note.  I  would  like  you  now  to  be  a1)le  to  speak  of  the 
chord  of  the  "sixth,"  meaning  the  first  inversion  of  the 
chord;  or  the  chord  of  the  "six  four,"  meaning  the  second 
inversion  of  the  chord,  as  those  are  terms  frequently  used 
by  musicians.  Remember  that  both  the  figures  and  the  inver- 
sions relate  only  to  the  l)ass  or  lowest  note,  and  do  not  in 
the  least  determine  which  note  shall  be  highest. 

95.  EAR-TRAIXING. 

As  you  play  (or  a  friend  plays)  the  chords  in  their 
different  inversions,  listen  intently  to  the  lowest  tone, 
trying  to  determine  whether  a  root,  third  or  fifth  is  in 
the  bass.  The  dift'erent  qualities  of  rest  or  incompleteness 
will  aid  in  determining  the  form  of  the  chord.  Remem- 
ber, however,  that  with  most  students  it  is  a  work  of 
months  to  gain  facility  in  these  lines.  But  if  you  learn  to 
listen  more  intelligently  as  you  play  or  hear  music,  you 
will  find  a  great  gain  in  musicianship  is  attained,  whether 
you  succeed  immediately  in  this  work  or  not.  To  aid  you 
in  distinguishing  the  v.arioiis  kinds  of  triads  by  hearing, 
the  followiuij-  niav  be  of  assistance. 


84  Graded  Lessons   in   Harmon ij 

Instead  of  trying  to  measure  the  tones  of  the  chord 
by  distance  or  by  trying  to  detect  which  tone  is  altered 
in  changing  from  Major  to  Minor,  Diminished  or  Aug- 
mented, it  is  better  to  listen  to  the  general  effect  or  color 
of  the  chord  and  try  to  notice  the  individual  qualities  of 
each  kind  of  triad. 

The  first  step  might  be  to  bring  the  chord  in  question 
into  one  of  the  great  groups  as  follows:  the  Major  and 
Minor  triads  are  restful,  that  is  consonant,  as  described 
at  the  end  of  Chapter  II,  H.  S.,  while  the  Diminished  and 
Augmented  triads  are  unrestful  or  dissonant  and  there- 
fore show  a  decided  tendency  to  progress  to  some  other 
chord.  So,  by  noticing  whether  the  chords  are  restful  or 
unrestful,  we  can  reduce  them  to  one  of  the  two  classes  in 
each  of  which  there  is  but  one  choice.  Let  us  suppose  we 
have  decided  the  chord  to  be  unrestful  or  dissonant :  It 
must  be  then  either  Diminished  or  Augmented.  The 
Diminished  triad  gives  a  sense  of  narrowness,  or  small- 
ness,  or  contraction,  and  if  we  listen  carefully  to  the  ten- 
dencies we  will  find,  if  the  triad  is  not  inverted  (and  for 
the  first  exercises  it  should  not  be  inverted)  that  they 
tend  to  approach  each  other,  the  upper  note  to  go  down- 
ward and  the  lower  note  to  go  upward.  In  the  Aug- 
mented triad  we  feel  the  effect  more  of  breadth,  and  the 
tendency  of  the  Augmented  fifth  is  to  go  upward  and  to 
expand.  In  this  way  we  can  distinguish  one  from  the 
other. 

To  distinguish  between  i\Iajor  and  Minor,  one  way  is 
to  listen  to  the  general  eft'ect  whether  cheerful  or  somber. 
The  Major  gives  the  eft'ect  of  floating,  or  of  brightness, 
while  the  Minor  gives  the  effect  of  depression,  or  sadness. 
Another  way  to  distinguish  between  ]\Iajor  and  iMinor 
triads  is  to  mentally  (or  audibly)  sing  the  three  tones  of  the 
triad,  beginning  with  the  lowest,  when  it  is  quite  easyto 
distinguish  whether  we  are  singing  1-3-5  of  the  Major 
scale  or  1-3-5  of  the  Minor  scale.  Experiment  along 
these  lines. 

96.  QUESTIONS  1-29,  Key.  pp.  09-70. 

Improvisation. 

97.  "BOUNDING"  AND  '•ROCKING"  CHORDS. 

In  Lesson  11  the  subject  of  "Bounding"  and  "Rocking" 
chords  was  introduced,  and  drill  was  given  upon  the  sim- 


(Iradcd    T.cssous    in    Ilarmonji  85 

I'k'i  fiirms  of  the  clioivl.  Tlic  stiuleiit  should  consider  Uiis 
the  Ijcgniniiig  of  a  most  important  work,  to  be  prosecuted 
(hiily  if  he  would  achieve  practical  success. 

DRILL. 

Go  over  each  exercise  in  the  various  lessons  upon  the 
chords  in  their  different  positions  and  inversions,  and 
make  a  thorough  drill  upon  each  exercise  in  every  Major 
key,  using  the  metronome  if  possible,  and  note  the  speed 
attained  in  each  exercise. 

WRITTEN  EXERCISES. 

Write  in  one  key,  a  complete  example  of  each  form  in 
which  you  practiced  the  above  exercises. 

KEYBOARD  DRILL. 

Repeat  the  above  exercises  in  all  Minor  keys  if  you 
are  an  advanced  student.  If  found  too  difficult,  this  work 
may  be  postponed  for  a  time. 

98.  KEYBOARD  DRILL. 

Return  to  H.  S.,  §105  and  try  to  connect  the  chords 
there  given,  continuing  the  use  of  the  "Bounding"  and 
"Rocking"  forms  which  you  have  learned.  This  should 
be  done  in  all  keys  including  Minor,  if  the  pupil  is  suf- 
ficiently advanced.  One  example  of  each  kind  and  of  all 
the  forms  where  special  difficulty  is  found  are  to  be  writ- 
ten out. 

Using  first  the  "Bounding"  and  then  the  "Rocking" 
chord  forms,  the  pupil  should  connect  chords  in  the  key 
of  C  in  the  following  order:  8,  6,  4,  2,  5,  3,  1 ;  that  is, 
connect  the  chord  of  C  Major  with  the  chord  of  A  Minor, 
which  in  turn  will  be  connected  with  the  chord  of  F 
Major,  which  in  turn  wnW  connect  with  the  chord  of  D 
Minor,  then  to  the  chord  of  G  Major,  then  to  E  Minor, 
then  to  C  Major.  (This  is  not  designed  as  the  conven- 
tional Closing  Formula,  which  will  come  later,  but  is  a 
practical  drill  in  employing  the  various  triads  of  the  key.) 

Repeat  this  exercise  in  both  "Bounding"  and  "Rock- 
ing" chord  forms  in  all  Major,  and  if  possible,  all  Minor 
keys. 

99.  REVIEW  AND  SYNOPSIS. 

At  this  point  the  pupil  should  review  triads  from  the 
beginning  and  should  write  a  complete  synopsis. 


86  (inidcd    Lessons    in    Ilarmon // 


LESSON  14. 

PART-WRITING— TRIADS. 

Connection  of  Triads  in  Simplest  Form. 

100.  STUDY. 

Skip  for  the  moment  H.  S.,  §§95-101.  Studv  //.  S., 
^§102-104  and  Key,  103. 

WRITTEN  EXERCISES. 

(  a )    Write  ten  examples,  H.  S.,  §105. 

(b)    Write  five  examples.     Transpose  to  other  keys. 

KEYBOARD  EXERCISES. 

Do  all  the  exercises  in  H.  S.,  §105,  (a),  (b)  and  (c). 

Special  Note.  This  lesson,  although  very  short  in  appear- 
ance, is  one  of  the  most  important  in  the  whole  course  and 
should  receive  many  hours  of  drill.  The  ambitious  student 
will  do  these  exercises  not  only  in  the  key  of  C  but  in  all 
other  keys.  He  will  also  do  them  with  the  left  hand  alone  as 
well  as  with  the  right  hand,  and  also  with  two  hands,  letting 
the  left  hand  take  tlie  l)ass  part,  as  illustrated  in  //.  -S".. 
Fig  30. 

To  Connect  Triads  When  There  Is  No  Common 
Note. 

101.  STUDY  H.  S.,  §§106-108. 
WRITTEN  EXERCISES. 

(1)  Copy  the  exercises  in  H.  S.,  §109,  and  fill  up  the 
vacant  parts  as  there  required. 

(2)  Write  the  exercises  in  H.  S..  §109,  (a)   and   (b). 

KRYBO.ARD  EXERCISES. 

Do  the  exercises  in  H.  S.,  §109,  as  shown  in  Fig.  32. 
Also  §109.  (a),  (b)  and  fc).     See  Key*,  p.  33,  Fi.g.  32. 

*HOW  TO  USE  THE  "KEY." 

SUGGESTION. 

(a)  In  doing  part-writing,  ii.  is  desirable  to  use  three  staves  for  each  exercise; 
write  the  liass  upon  the  lower  one  of  the  three,  your  own  setting  upon  the 
middle  staff,  and  reserve  the  upper  staff  for  the   Key.  ropyint;  in  from  the  Key 


(inided    l.csKoiis    in    Ihi rmoii //  87 

102.  SI'UDV  //.  S.,  §§95-101;  also  Key,  pp.  l".)-32. 

WRITTEN'   EXERCISES. 

Now  go  over  the  written  exercises  already  completed 
for  this  recitation,  examine  to  find  the  consecutive  fifths 
and  octaves,  and  correct  the  same  as  best  you  can. 

103.  QUESTIONS  (J,  7.  S,  13,  Key,  p.  71. 


only  those  chords  which  differ  from  your  own  setting.  Be  sure  to  have  the  bar 
lines  go  through  the  three  staves,  so  that  the  copied  chords  from  the  Key  will 
be  over  the  proper  bass  notes.  This  plan  not  only  brings  the  Key  setting  into 
proper  place  for  easy  comparison  with  your  own  but  it  is  essential  for  future 
reference  and  study.  It  also  makes  it  easy  to  discuss  the  advantages  of  one 
setting  over  the  other  and  it  makes  a  deeper  and  more  musicianly  worker 
of  yourself. 

(b)  Pupils  are  placed  upon  their  honor  not  to  consult  the  Key  until  after 
the  part-writing  or  other  exercises  under  consideration  are  completed.  Then 
as  the  next  step  they  are  to  compare  their  work  with  the  solution  in  the  Kfv: 
Nnle  each  difference  and  give  the  reason  in  writinn: 

(1)  For  the  superiority  of  the  setting  in  the  Key; 

(2)  For  the  (possible)  superiority  of  his  own  setting; 

(3)  For  the    acceptability  of  both   settings,  if  possible;    and    if   you 
think  a  still  different  setting  could  be  used,  tell  why. 

This  process  saves  the  teacher  time  in  the  routine  clerical  work  of  writing 
out  a  correct  solution  and  brings  the  discussion  right  to  the  points  of  difficulty; 
making  possible  a  much  more  thorough  and  searching  discussion  of  underly- 
ing principles  than  is  possible  in  re-writing  an  incorrect  exercise.  To  make 
such  discussion  with  a  class  is  most  educational.  This  removes  the  danger 
of  the  pupil's  having  a  Key.  for  its  use  becomes  a  part  of  the  educational  process 
and  forces  him  to  find  underlying  reasons  and  principles. 


88  (.iradcd   Lessons    in    Ilannonij 

LESSON  15. 

PART-WRITING— TRIADS  (Cont.) 

104.  NOTE. 

We  now  come  to  a  new  department  of  our  work — the  only 
one  recognized  in  older  methods,  but  which  is  only  one  of 
several  important  departments  in  their  course.  "Part-writing" 
means  writing  chords  from  a  given  bass  or  from  a  given 
melody,  the  latter  being  commonly  called  "Harmonizing  Melo- 
dies." 

The  older  methods  gave  us  many  positive  rules,  chiefly 
prohibitions,  for  part-writing,  and  then  furnished  so  many 
exceptions  to  each  rule  that  the  average  student  became  be- 
wildered and  lost  all  confidence.  In  this  course  it  will  be 
attempted  to  shozv  the  principles  zvhich  govern  not  only  the 
applications  but  also  the  exceptions  to  the  rules.  But  the 
student  must  remember  that  skill  in  part-writing  is  less  a 
matter  of  rule  than  of  judgment,  or  a  balancing  of  one  force 
against  another, — a  steering  one's  boat  along  a  channel  filled 
with  obstacles,  where  in  steering  around  one  rock  we  must 
be  careful  not  to  collide  with  another. 

The  work  in  part-writing  is  in  a  certain  sense  like  a  review 
of  the  subject,  since  we  return  to  the  subject  of  triads  and 
cover  the  same  ground  as  before,  but  with  a  different  end  in 
view.  While  the  exercises  in  part-writing  are  being  carried 
on,  the  student  should,  without  fail,  make  a  thorough  review 
of  all  the  constructive  work  at  the  keyboard  covered  in  the 
previous  lessons.  These  exercises  should  now  be  carried  into 
more  difficult  keys,  and  higher  speed  and  more  accurate  think- 
ing should  be  required. 

STUDY  H.  S.,  §§1G1-169 ;  also  Key,  pp.  64-67. 

Note.  The  above  pages  should  give  the  student  a  general 
idea  of  the  principles  of  part-writing  which  will  make  the 
corrections  of  the  written  work  more  intelligent. 

Ri-:\'IRW  //.  s..  ^o:,-^^^. 


Ciradcd    Lessons    in    TIdnuon  1/  80 

WRITTEX  EXERCISr.S.* 

(a)  Write  the  exercises  in  H.  S.,  §11.">.  Compare  witli 
Key,  pp.  Ho-l'A.  ( For  best  results,  do  not  consult  Key 
imtil  all  the  exercises  arc  written.) 

(b)  Write  the  exercises  in  H.  S.,  §11G,  then  compare 
with  Key,  pp.  3G-38. 

How  to  Discover  Consecutive  Fifths  and  Octaves  in 

the  Written  Work. 

105.  Very  frequently  students  do  not  know  how  to  go  to 
work  to  find  consecutive  fifths  and  octaves  in  the  written 
exercises.  The  following  will  be  found  of  great  assist- 
ance: A  consecutive  fifth  or  octave  implies  that  the  in- 
terval of  a  fifth  or  octave  shall  have  appeared  between 
the  same  voices  in  two  consecutive  chords.  The  first  thing 
is  to  understand  what  the  term  "same  two  voices"  means. 
It  is  this:  If  between  the  Bass  and  Tenor  of  a  chord  the 
interval  of  a  fifth  is  found,  and  the  same  interval  is 
found  between  the  same  two  voices  in  the  next  chord  fol- 
lowing, consecutive  ~  fifths  have  been  formed.  On  the 
other  hand,  if  in  the  first  chord  the  fifth  is  between  the 
Bass  and  Alto,  while  in  the  second  chord  the  fifth  is 
between  the  Bass  and  Tenor,  they  cannot  be  called  con- 
secutive fifths,  since  consecutive  fifths  require  that  the 
interval  shall  be  found  between  the  same  two  voices  in 
consecutive  chords.  (Of  course,  in  the  above  illustration 
other  voices  than  Bass  or  Tenor  could  be  used.  The  chief 
point  is,  that  whichever  voices  have  the  octave  or  fifth 
in  the  first  chord,  must  have  it  in  the  next  chord  to  make 
the  fifths  or  octaves  consecutive.) 

The  student  should  remember  especially  that  a  fifth 
in  a  single  chord  is  not  wrong,  nor  are  octaves  or  fifths 


♦NOTE  TO  TEACHERS. 

The  work  in  part-writing  should  be  even  more  personal  and  individual 
than  the  preceding  work,  for  the  exercises  written  by  the  student  must  be 
carefully  corrected. 

NOTE  TO  STUDENTS, 

Part-writing  is  a  matter  oi  facility,  and  we  need  to  do  work  not  only  correctly, 
but  quickly.  The  best  way  to  gain  the  desired  results  is  to  take  a  limited 
number  of  exercises,  not  more  than  six  or  eight,  and  write  them  once  through. 
The  next  day  do  the  same  work  without  reference  to  the  work  of  the  day  before. 
Repeat  this  every  day  for  a  week.  Remember  that  your  jirogress  is  not  measured 
by  the  length  of  the  lesson  but  by  the  way  in  which  it  is  studied;  that  is,  by 
repealed  workings  of  each  exercise. 


90  (iradcd    I.c.ssotis    in    1 1  a  nnan  1/ 

wrong  ill  two  successive  chords,  but — and  here  is  the 
great  point — they  must  not  appear  l)etween  the  same 
\oices  in  both  chords. 

SPECIA[.  DIRECTIONS. 

When  writing  an  exercise,  as  soon  as  each  exercise  is 
written  the  student  should  stop  and  examine  the  progres- 
sion  from  the  previous  chord   somewhat  as  follows : 

Are  there  consecutive  fifths  or  octaves  formed  between 
Bass  and  Tenor  ? 

Are  there  consecutive  fifths  or  octaves  formed  between 
Bass  and  Alto? 

Are  there  consecutive  fifths  or  octaves  formed  between 
Bass  and  Soprano? 

Are  there  consecutive  fifths  or  octaves  formed  between 
Tenor  and  Alto? 

Are  there  consecutive  fifths  or  octaves  formed  between 
Tenor  and  Soprano? 

Are  there  consecutive  fifths  or  octaves  formed  between 
Alto  and  Soprano  ? 

In  this  way  the  student  will  learn  to  watch  the  leading 
of  the  voices  almost  unconsciously  and  so  avoid  the  pit- 
falls of  consecutive  fifths  and  octaves. 

STUDY  //.  .9..  §§07-111,  and  Key.  pp.  29-32. 
10(5.   (JUICSTIOXS  1-5,  Key,  ]>.  71. 


(lidded    I.rxxoii.s    in    Ifdrmoiii/  91 

LESSON  16. 

PART-WRITING— TRIADS   (Com.) 

Kii.  After  writing  tlu-  exercises  required  in  Lesson  15, 
the  student  is  urgently  advised  to  read  again  //.  S.. 
§§95-114,  and  §§161-1(!9;  Key,  pp.  29-;^>2,  64-67. 

WRITTEX   EXERCISES. 

Write  the  exercises  in  //.  .S".,  §12<».      (See  Key.  p.  42.) 

To  Avoid  the  Augmented  Second  From  6  to  7  of  the 
Minor  Scale. 

108.  STUDY.  Students  often  have  difficulty  at  this  point, 
so  the  following  statements  must  be  as  emphatic  as  pos- 
sible. To  avoid  the  Augmented  second,  the  seventh 
must  be  approached  from  above;  or  at  least  if  from  below 
it  must  be  by  a  skip ;  that  is,  we  must  not  proceed  directly 
from  6  to  f.  Please  heed  this.  We  can  go  from  5  to  7. 
but  not  from  6  to  7.  It  is,  however,  better  to  go  from 
8  to  7. 

If  you  find  that  you  have  made  this  mistake  you  can 
correct  it  bv  changing  the  voice  that  moves  to  7.  For 
example,  take  the  chord  D-F-B,  followed  by  E-G*-B,  here 
you  see  the  Alto  of  the  first  chord,  F,  has  moved  an 
Augmented  second  to  Gtt  in  the  second  chord;  to  correct 
this,  let  the  Soprano  proceed  to  Gi+  and  let  the  Alto  go 
downward,  making  the  second  chord  B-E-GS.  Now  you 
will  see  that  we  have  followed  the  rule  to  let  a  different 
voice  approach  7.  You  will  see  that  the  Alto  which  in 
the  first  example  made  the  Augmented  second  upward. 
now  makes  a  half-step  downward.  Do  not  be  confused 
by  the  fact  that  G*  is  in  the  second  chord  and  F  is  in  the 
first  chord.  This  does  not  make  the  Augmented  second 
unless  the  same  voice  sings  both  tones. 

READ  Key,  p.  43,  and  do  the  Additional  Exercises  as 
outlined. 

\VRTTE  the  exercises  from  the  Figured  Bass  in  //.  S.. 
§120.     (See  Key.  12^,,  pp.  4:1-49.) 


92  Graded   Lessons    in    Ilannou  1/ 

1<'9.  KEYBOARD  EXERCISES. 

Working  from  the  Bass  in  H.  S.,  §§115-Ii<'>,  try  to  play 
ihc  required  chords  with  the  right  hand.  \Vork  slowly 
at  first  and  try  to  make  the  individual  voices  move  as 
smoothly  as  in  the  written  exercises. 

110.  SPECIAL  NOTES. 

(1)  Doubling  the  Third.  One  of  the  most  frequent  diffi- 
culties encountered  by  the  student  is  to  know  when  to  double 
the  third  in  a  chord  and  when  not  to  do  so.  The  question 
is  thoroughly  answered  in  //.  5.,  §§162-166,  and  in  Kcv,  162- 
166,  pp.  64-66. 

(2)  Conceniing  tJie  Rule  Which  Required  the  Common 
Note  to  Remain  in  the  Same  J^oice.  This  difficulty  is  fre- 
quently encountered  but  will  be  conquered  in  a  very  short 
time.  Study  H.  S.,  §167,  carefully.  Sometimes  by  changing 
the  position  of  a  previous  chord,  the  common  note  may  be 
so  managed  as  to  remain  in  the  same  voice,  bvit  it  frequently 
happens  in  a  cadence  (the  chord  of  the  Dominant  seventh 
followed  by  the  Tonic)  that  this  rule  must  be  broken.  Read 
pp.  35-36  in  Key. 

(3)  Ho-cV  to  Choose  Bctu'een  Tico  Possible  Progressions. 

(a)  Look  ahead  to  see  how  the  following  chords  will  take 
shape,  measuring  the  comparative  smoothness  of  the  two  ways. 

(b)  Study  the  tendencies  of  the  individual  tones  contained 
in  the  chord,  particularly  of  the  outer  voices.  It  is  quite  pos- 
sible that  the  progression  in  which  the  tendencies  of  the  indi- 
vidual tones  are  best  observed  will  be  the  better  progression. 
Rut  in  this  progression  do  not  forget  the  "Tendency  of  Con- 
tinuity" as  that  very  frequently  overrules  the  melodic  ten- 
dencies of  the  tones  of  the  chord. 

Hidden  Fifths  and  Octaves. 

111.  XoTE  1.  Students  frequently  have  trouble  to  discover 
consecutive  or  hidden  fifths  and  octaves  in  their  work  unless 
especial  attention  be  given  to  the  point.  Let  us  begin  with 
a  conventional  definition  of  the  term  "Hidden  Fifths." 

Definition.  "When  two  voices,  moving  in  the  same 
direction,  arrive  at  the  interval  of  a  fifth,  Hidden  Fifths 
are  produced."  (The  student  will  please  learn  the  fore- 
going definition  by  heart.) 

Note  2.  Tests  in  the  classroom  prove  conclusively  that 
with  such  a  definition  as  the  above  not  one  student  in  five 
will  get  a  complete  and  correct  impression  until  the  individual 
points  are  brought  out  by  the  teacher's  questions.     Read   the 


Graded  Lessons   in  Ilarmoni/  93 

above  definition  carefully  and  then  see  if  the  points  mentioned 
below  are  already  in  your  mind,  or  whether  the  following 
description  helps  to  give  a  clear  impression. 

DESCRIPTION  OF  THE  ABOVE  DEFINITION. 

(a)  "When  two  voices."  Note  that  two  voices  are 
indicated.  By  this  is  meant,  not  that  any  two  voices  may 
start  to  progress  in  the  same  direction  and  some  otiicr 
voices  arrive  at  the  interval  of  a  fifth,  but  that  the  same 
two  voices  shall  progress  in  a  similar  direction  and  arrive 
at  the  interval  of  the  fifth. 

(b)  ''Moving  in  the  same  direction."  It  will  never 
be  a  hidden  fifth  if  two  voices,  moving  by  contrary  or 
oblique  motion,  strike  the  interval  of  a  fifth, 

(c)  "Arrive  at  the  interval  of  a  fifth."  This  does 
not  mean  that  the  first  of  the  two  intervals  may  be  a 
fifth  and  the  second  interval  something  else,  but  that 
the  first  shall  be  "something  else"  and  the  latter  of  the 
two  intervals  shall  be  a  fifth. 

NoTC*.  Many  students  do  not  thoroughly  understand  hid- 
den fifths  and  octaves.  A  hidden  fifth  occurs  where 
two  notes  which  are  not  a  fifth  apart  moving  in  the  same 
direction  rest  upon  a  fifth.  For  example :  Play  the  notes 
D-B.  If  B  moves  upward  a  half-step  to  C,  and  D  moves 
upward 'two  degrees  to  F,  a  hidden  fifth  will  be  produced. 
Note  the  following  points : 

(1)  The  notes  must  not  be  a  fifth  apart,  since  there  would 
be  open  or  consecutive  fifths  if  the  interval  of  a  fifth  were 
found  both  in  the  first  and  last  interval. 

(2)  They  must  move  in  the  same  direction ;  that  is,  both 
must  go  up  or  both  go  down.  If  two  notes  moving  in  con- 
trary motion  should  arrive  at  the  interval  of  a  fifth  it  could 
not  be  considered  a  hidden  fifth. 

Further,  if  one  note  should  remain  still  and  the  other  move 
to  the  interval  of  a  fifth,  it  could  not  be  considered  a  hidden 
fifth. 

(3)  The  second  of  the  two  intervals  must  be  the  fifth, 
not  the  first. 

SPECIAL   NOTE. 

It  should  be  rcmcml)ercd  that  all  hidden  fifths  and 
octaves  are   not    faultv.     On  the  contrarv,   many   hidden 


*  From  special  lessons  to  pupils,  1913. 


94  drach'd   Lessons    in    Ihtrmoiii/ 

fifths  and  octaves  must  be  used  else  the  progression  will 
be  angular  and  awkward.     The  faulty  hidden  fifths  are : 

(1)  Those  in  which  both  parts  skip  (where  one  voice 
moves  diatonically  the  hidden  fifth  or  octave  is  usually 
agreeable  and  therefore  allowed)  ; 

(2)  Those  which  in  their  effect  contradict  the  melodic 
or  the  harmonic  tendencies  (the  effect  is  likely  to  be  dis- 
agreeable and  therefore  faulty). 

The  student  should  read  H.  S.,  §§134,  1(J3,  105;  also 
Key.  134,  PI).  (i2-()4. 

NoTi:*.  14idden  octaves  and  hidden  fifths  are  not  always 
bad.  To  avoid  them  in  every  case  will  often  result  in  pro- 
ducing worse  faults  in  the  awkward  progressions  arising. 
There  are  many  rules  in  various  hooks  concerning  which 
hidden  octaves  and  fifths  are  permitted  and  which  are  not 
permitted.  The  following  to  my  mind  covers  the  ground  with 
sufficient  thoroughness  for  all  practical  purposes : 

(1)  Hidden  fifths  or  octaves  in  which  both  voices  skip 
are  not  good  and  should  not  be  used.  In  connection  with  this 
point,  it  should  be  remembered  that  the  outer  voices  are 
more  prominent  than  the  inner  voices,  and  that  which  might 
sound  badly  in  the  Soprano  is  sometimes  quite  satisfactory 
when  found  in  the  Tenor  or  Alto. 

(2)  Where  the  natural  melodic  tendencies  of  the  scale 
tones  are  disregarded,  the  effect  of  the  hidden  fifth  or 
octave  is  usually  not  good,  and  such  hidden  fifths  or 
octaves  should  not  be  employed.  It  may  be  observed  that 
the  natural  tendency  of  a  scale  tone  is  brought  more  into 
prominence  by  the  hidden  fifth,  or  octave,  and  that  which 
might  have  passed  unnoticed  under  ordinary  circumstances 
is  developed  through  tlie  doubtful  progression  into  a  positive 
fault.  So  it  is  my  plan  to  judge  the  hidden  fifths  and 
octaves  by  the  above  tests,  whether  both  voices  skip,  and 
whether  any  tendency  is  violated.  If  these  tests  are  met  I 
admit  the  hidden  fifth  or  hidden  octave  as  correct. 

EXERCISES.  Write  three  examples  showing  hid- 
den fifths,  making  as  much  variety  in  the  form  as  you 
can. 

Hidden  octaves  arc  described  similarly  to  hidden  fifths. 

EXERCISES.  Write  three  examples  of  hidden 
octaves. 

Should   vou,   after  this,    fail   to  miderstanij    tliorougbl\ 

*  l'"roni  a  siHcial  lesson  to  a  imiiil,  1'M.v 


(iradcd   Lessons    in    Ilurmoui/  95 

the  hitUlen  fifths  and  octaves,  read  the  above  twice 
carefully.  Also  study  again  //.  5"..  §134,  and  Key,  134, 
pp.  (!2-G4. 

COLLATERAL    READING. 

112.  (1)  Statement.  Broken  Chords.  The  notes  of  a 
chord,  instead  of  sounding  together,  may  be  given  in 
succession,  and  in  any  desired  order,  with  any  desired 
duplication  of  notes,  and  through  as  many  octaves  as 
desired.  For  example,  an  arpeggio  is  simply  a  broken 
chord  led  through  several  octaves.  Similarly,  the  left 
hand,  in  much  piano  music,  performs  chiefly  broken 
chords.  It  is  important  to  realize  that  these  extended 
forms  are  usually  nothing  more  than  simple  chords. 

(2)  Exercises. 

(a)  Form  examples  of  as  many  different  figures  in 
broken  chords  as  possible. 

(b)  Look  for  examples  of  broken  chords  in  instru- 
mental music. 

(3)  Statement.  To  find  the  root  of  an  inverted  triad 
or  chord  of  the  seventh.  Continue  to  invert  (try  in  dif- 
ferent inversions)  until  the  intervals  of  a  third  and 
fifth  are  found  for  the  triad,  or  of  a  third,  fifth  and  sev- 
enth for  a  chord  of  the  seventh.  The  lowest  note  will 
then  be  the  root  of  the  chord. 

OBSERVATIONS. 

(Study  the  following  with  special  care.) 

(4)  Of  Chord  Individuality.  It  should  be  noted  that 
the  identity  of  a  chord  is  not  destroyed  by  inversion,  or 
by  adding  more  notes,  although  the  characteristic  form 
and  appearance  of  the  chord  may  be  entirely  altered. 
The  principal  chords  of  a  scale  retain  their  relative  im- 
portance. \vhether  appearing  in  the  form  of  a  triad,  chord 
of  the  seventh,  chord  of  the  ninth.  Diminished  seventh 
or  Augmented  sixth.  Similarly,  an  unimportant  chord 
retains  its  relative  condition  in  any  of  the  above  mentioned 
forms.     So  the  individuality  of  a  chord  is  never  lost. 

(5)  Of  Chord  Connections.  Governing  the  connec- 
tions and  use  of  common  chords,  there  appear  to  be  sev- 
eral important  influences  at  work,  somewhat  as   follows: 


96  Graded   Lessons   in   Ilarrnonj/ 

(a)  There  is  a  physical  connection  between  differ- 
ent triads  or  common  chords,  regardless  of  their  asso- 
ciation in  a  key,  which  is  caused  by  the  fact  that  there 
are  notes  common  to  both  chords.  (Note.  It  is  largely 
owing  to  this  fact  that  different  keys,  apparently  unrelated, 
can  be  connected  in  a  smooth  manner.) 

(b)  There  is  a  latent  connection  or  relation  be- 
tween chords  which  have  no  common  note  or  notes,  when 
they  are  members  of  the  same  key.  (Note.  It  is  this  fact 
that  explains  the  connection  of  two  triads  which  have  no 
note  in  common,  as  for  example,  in  connecting  the  triad 
of  C  Major  with  that  of  D  Minor,  the  first  and  second 
degrees  of  the  key  of  C.) 

(c)  There  is  a  certain  conventionality  about  the 
succession  of  chords,  which  seems  to  proclaim  certain  pro- 
gressions good  and  others  bad.  That  which  makes  many 
progressions  disagreeable,  and  forbidden  in  Harmony 
text-books,  is  that  some  harmonic  or  melodic  ten- 
dency is  thereby  violated.  (The  writer  will  attempt 
to  show  later  how  the  melodic  and  harmonic  tendencies 
already  described  control  all  of  the  regular  resolutions  in 
music,  and  also  explain  the  origin  and  reasonableness  of 
many  otherwise  inexplicable  rules  of  harmony.)  This 
conventional  line  of  progression  of  chords  may  be  corn- 
pared  to  the  idiomatic  form  of  language,  where  certain 
expressions,  in  themselves  perfectly  correct,  seem  strange, 
for  the  reason  that  they  do  not  follow  the  idiomatic  form. 
When  the  student  appreciates  this  conventional  forrn  of 
expression  he  will  be  able  to  comprehend  many  things 
which  are  not  fully  clear  as  the  operation  of  principle. 

(d)  The  writer  is  inclined  toward  the  belief  that 
tonality,  or  key.  is  largely  the  result  of  the  natural  affin- 
ity of  certain  chords  for  each  other,  and  not  the  contrary, 
i.e..  that  chords  are  related  for  the  reason  that  they 
happen  to  be  in  the  same  key.  This  presumption  is  illus- 
trated most  forcibly  by  the  'fact  that  in  the  development 
of  music  the  feeling  of  tonality  was  exceedingly  vague,  as 
well  as  the  use  of  signatures,  until  the  chord  of  the  Domi- 
nant seventh  was  introduced.  The  use  of  this  chord, 
although  against  the  judgment  of  the  musicians  of  the 
day,  brought  a  distinct  impression  of  tonality. 

'  (6)  Of  the  Correlative  Character  of  the  Different 
Chord  Forms.  Referring  to  Collateral  Reading.  §5^. 
(7)-(8),  it  is  found  that  Major  intervals  when  inverted 


Graded   Lessons   in   Ilarmonif  97 

become  Minor,  Minor  become  ■Major,  Diminished  become 
Augmented,  and  Augmented  become  Diminished.  Further, 
it  is  found  that  Major  and  Minor,  and  Augmented  and 
Diminished,  are  correlative  terms;  that  is,  when  a  Major 
interval  becomes  Minor  by  inversion,  it  remains  in  the 
same  class  as  before;  i.e.,  if  the  given  Major  interval  is 
consonant,  its  correlative  Minor  will  also  be  consonant, 
while  if  the  given  Major  is  dissonant,  its  correlative  Minor 
will  be  dissonant.  And  similarly,  the  Augmented  and 
Diminished  intervals  are  correlative.  Applying  the  fore- 
going to  the  structure  of  chords,  it  will  be  noticed  that 
when  a  triad,  for  example,  is  inverted,  some  of  its 
component  intervals  are  thereby  inverted.  But  as  the 
inversion  of  an  interval  does  not  alter  its  quality  of 
consonance  or  dissonance,  so  the  inversion  of  a  chord 
does  not  alter  its  quality  of  consonance  or  disso- 
nance, on  account  of  this  wonderful  correlative  quality 
in  its  component  intervals.  To  illustrate  this  point, 
consider  the  simplest  triad,  C-E-G.  C-E  is  a  Major 
third,  which  by  inversion  becomes  a  IMinor  sixth,  E-C. 
Xow,  if  the  Major  third  and  Minor  sixth  were  not  both 
members  of  the  consonant  family  (or  if  they  were  not 
correlative),  the  inversion  of  the  triad  would  change  it 
from  a  consonant  to  a  dissonant  triad,  and  so  change  all 
its  relations  with  other  chords.  It  is  by  such  facts  as  the 
above  that  a  clear  impression  is  gained  of  the  symmetry 
and  logical  completeness  of  the  structure  of  music. 

(7)  Frequent  reviews  of  the  subject,  independent  of 
any  interruption,  are  of  great  assistance  in  keeping  in  mind 
the  thread  of  thought,  the  logical  development  of  one  prin- 
ciple from  another.  A  most  important  aid  in  a  review 
is  to  make  a  careful  synopsis  of  each  subject;  that  is,  of 
scales,,  of  intervals,  of  triads.  Illustrations  of  these 
synopses  may  be  found  at  the  end  of  several  chapters  of 
H.  S.  and  the  Key.  It  is  not  necessary  to  construct  a 
synopsis  from  memory,  but  rather  from  the  text,  compar- 
ing one  section  with  another,  until  the  relations  of  the 
parts  to  each  other  are  discovered,  and  the  logical  out- 
growth of  one  thought  into  another  is  understood.  Facts 
and  principles  do  not  stand  alone,  but  one  leads  to  another, 
making  a  chain  of  logic,  which,  when  understood,  is  per- 
fectly simple.  This  is  most  particularly  the  case  with  our 
subject,  and  the  student  is  urged  to  find  this  thread,  which 
will  make  this  a  most  fascinating  and  profitable  study. 


98  iirudcd   Lessuii.s    in    Harmon  1/ 

(8)  Exercises,  (a)  Refer  to  the  previous  lessons, 
read  the  text  carefully  and  thoughtfully,  and  do  every 
exercise,  choosing,  if  possible,  different  keys  from  those 
used  before. 

(b)  Make  a  synopsis  of  scales,  of  intervals,  and  of 
triads,  first  referring  to  the  examples  mentioned  above, 
and  then  proceeding  from  the  text.  Afterward  compare 
with  the  synopses  in  H.  S.  and  Key.  (N.B.  Work  of 
this  nature  will  greatly  assist  the  memory  in  retaining  the 
foundation  principles  of  harmony.) 

(9)  Exercises.  Drill  yourself  in  the  formation  of 
various  intervals  and  triads,  in  every  key,  continuing  until 
perfect  familiarity  and  good  speed  are  attained.  (N.B. 
This  familiarity  with  the  formation  of  all  kinds  of  triads 
is  indispensable  in  the  more  complicated  forms  of  later 
study,  for  if  the  simple  forms  are  not  under  control  the 
larger  forms  developed  from  them  will  simply  be  impos- 
sible in  any  practical  and  useful  sense.) 

(10)  In  the  drill  for  review,  particular  attention 
should  be  given  to  the  connection  of  triads.  Unlike  other 
methods  of  harmony  study,  it  is  here  intended  that  the 
student  shall  learn  to  connect  triads  at  the  keyboard.  This 
is  a  direct  step. toward  the  realization  of  one  of  our  sub- 
jects: viz.,  to  be  able  to  use  the  knowledge  of  the  theory 
and  structure  of  music.  Detailed  directions  of  much  value 
to  the  beginner  in  chord  connection  may  be  found  in 
H.  S.  and  Key. 

(11)  Exercises,  (a)  Taking  the  dift'erent  keys  in 
turn,  connect  the  triads  upon  the  first  degree  with  the 
triads  on  as  many  other  degrees  of  the  same  key  as 
possible. 

(b)  Connect  the  triad  on  the  second  degree  with 
as  many  other  triads  in  the  same  key  as  possible. 

(c)  Continue  similarly  from  each  of  the  remaining 
degrees  of  the  scale  and  repeat  in  other  keys. 

113.  QUESTIONS  9-12,  14-29,  Key.  pp.  71-72. 

(In  Lesson  27  you  will  later  be  asked  ti>  answt-r  <Jues- 
tions  14-29  more  completely.) 


(iiddcd    Lessons    in    /Iiirmon if  99 


LESSON  17. 

PAR'l-WRITING— IRIADS   (Cont.) 

114.  l''ollo\ving  the  directions  about  using  the  Kcv  (see 
Lesson  14),  write  Exercise  1.  H.  S.,  §133,  compare  with 
Key,  p.  57  and  write  your  opinion  of  cz'cry  point  of  differ- 
ence immediately  under  your  work.  Proceed  similarly 
with  the  remaining  exercises  of  §133. 

Should  you  find  any  difficulty  in  interpreting  the  fig- 
ures, refer  to  the  Key.  p.  54,  and  study  pp.  54-56,  giving 
especial  attention  to  the  exercises  there  found. 


100  Graded   Lessons   in   Ilarmonj/ 

LESSON  18. 

PART-WRITING— TRIADS  (Cont.) 

115.  In  future  each  part-writing  exercise  as  soon  as 
completed  should  be  compared  with  the  Key  and  your  ob- 
servations made  upon  each  point  of  difference,  as  shown 
in  the  directions  on  "How  to  Use  the  Key,''  Lesson  14. 
Following  this  plan,  work  the  exercises  in  H.  S.,  §131. 

X.B.  Do  not  harmonize  the  scales  at  present.  This  is  de- 
signed for  a  later  lesson. 

A  Little  Lesson  in  Transposition. 

IIG.  The  secret  in  transposition  is  to  recognize  locations  in 
the  key  and  to  be  able  to  express  corresponding  locations 
in  any  required  key.  The  proper  preliminary  study  of  the 
relative  names  (Tonic,  Super-tonic,  jMediant,  etc.),  or  of 
the  scale  degrees  (first,  second,  third,  fourth,  etc.),  and 
the  subconscious  recognition  of  these  relative  names  will 
go  far  toward  making  transposition  easy.  Commence  with 
the  transposition  of  melodies.  If  the  melody  can  be  car- 
ried in  the  mind  and  mentally  or  audibly  sung  while  being 
written  it  will  make  the  best  possible  drill.  Let  us  take 
for  example  the  melody  of  "Old  Hundred."  E^xpressed  in 
figures  (without  the  rhvthm)  it  will  be:  1,  1,  7,,  6,,  5,,  1, 
2,  3 ;  3,  3,  3,  2,  1,  4,  3,  2 ;  1.  2,  3,  2,  1,  G„  7,,  1 ;  5,  3,  1,  2, 
4,  3,  2,  1. 

The  pupil  should  first  mentally  sing  this  through, 
trying  to  associate  the  numerals  with  the  tones  of  the 
melody  and  with  the  notes,  as  written,  for  example,  in  the 
key  of  G.  After  doing  this  try  to  write  it  in  the  key  of 
F,  mentally  singing  the  melody  with  the  appropriate  num- 
bers. Now  write  it  successively  in  every  ]\Iajor  key — first 
without  the  signature,  that  is,  writing  in  each  sharp  or 
flat  as  required,  and  afterward  writing  the  signature  in 
its  place.  Similarly  write  in  four  different  keys  two  dif- 
ferent melodies,  f(n-  example,  "(^Id  I'olks  at  Home"  and 
"^'ankee  Doodle." 


Graded   Lessons   in    llarmoni/  101 

LESSON  19. 

CHORDS  OF  THE  SEVENTH. 

117.  STUDY  H.  S.,  §§147-149,  and  Key,  147,  p.  73. 

COLLATERAL  READING.     §122,  (l)-(6)   inclusive. 

Spixial  Xote.  Remember  that  in  formins:  chords,  alter- 
nate letters  are  used.  This  applies  to  chords  of  tiu-  seventii 
just  as  nnich  as  to  triads. 

DRILL. 

What  letters  are  required  to  build  a  chord  of  the  sev- 
enth upon  each  of  the  following  notes  used  as  a  root 
(remember  that  sharps  and  flats  are  not  required,  but  oidv 
the  letter  name)  :     G?     D?     B?     F?     A?     C?     E? 

XoTF..  As  chords  of  the  seventh  may  he  built  upon  each 
and  every  note  of  the  scale,  it  is  necessary  to  l)econie  practi- 
cally familiar  with  this  point,  through  the  following. 

EXERCISES.     H.  S.,  §148,  (a),  (b),  (c)  ;  write. 

Compare  the  various  chords  of  the  seventh  in  the  key. 
as  described  in  H.  S.,  §149,  and  required  in  the  following-. 

118.  EXERCISES. 

Analyze  all  the  chords  of  the  seventh  in  the  key  of 
G,  describing  in  each  case  the  third,  fifth  and  seventh 
(that  is,  stating  whether  Major  or  Minor,  etc.). 

OBSERVATIOX. 

The  student  should  observe  that  the  chord  of  the  seventh 
upon  the  fifth  degree  of  the  scale  is  more  agreeable  and  satis- 
factory than  the  others.  The  fifth  degree  of  the  scale  is  called 
the  Poiiniiaiit,  and  the  chord  of  the  seventh  upon  the  fifth 
degree  is  called  the  chord  of  the  Dominant  seventh.  (The 
reason  for  this  term  "Dominant"  will  appear  in  a  later  lesson.) 


102  (lidclcd   Lessons    iti    Iltirrnoii  1/ 

ll!t.  KEYBOARD  EXERCISES. 

Form  the  chords  of  the  Dominant  seventh  in  every 
key.  proceeding-  systematically  from  key  to  key.  Note 
specifically  whether  you  can  strike  all  the  notes  of  the 
chord  instantly,  or  whether  you  hesitate  in  some  of  the 
keys.     Use  the  metronome. 

WRITTEN  EXERCISES. 

Write  the  chord  of  the  Dominant  seventh  in  every  key. 
Re  sure  that  the  chords  you  play  correspond  with  the 
written   forms. 

120.  EAR-TRAIXING. 

(a)  Play  a  Major  triad  and  immediately  afterward 
add  the  Minor  seventh,  changing  it  into  a  chord  of  the 
Dominant  seventh.  Xote  very  carefully,  the  restfulness 
of  the  triad  and  the  lack  in  the  chord  of  the  seventh. 

(b)  Ask  a  friend  to  play  triads  and  chords  of  the 
seventh  while  you  try  to  distinguish  one  from  the  other, 
liy  observing  the  quality  of  rest  or  its  absence. 

(c)  Listen  very  intently  for  this  point  when  hearing 
music  performed. 

121.  QUESTIONS  1-10,  Key,  p.  81. 

COLLATERAL  READING. 

122.  (1)  The  chord  of  the  seventh  may  be  said  to  repre- 
sent, as  a  type,  the  great  family  of  dissonant  chord  struc- 
ture. As  such  the  chord  suggests  motion,  as  contrasted 
with  the  rest  of  the  consonant  triad.  (See  Collateral 
Reading,  §('»(),  [2]-[l].)  It  represents  labor,  and  strife, 
and  longings,  which  are  satisfied  when  it  is  "resolved"  or 
led  in  a  natural  way  into  the  condition  of  consonance. 

For  the  student,  as  for  the  scientist,  it  forms  one. of 
the  most  important  parts  of  harmony  study,  for  it  epito- 
mizes within  itself  most  of  the  principles  of  musical 
structure  and  the  relations  of  the  tone  world.  Think 
about  this  last  statement. 

(2)  Construction  of  the  chord  of  the  seventh.  State- 
ment. It  is  formed  from  the  triad  by  adding  another 
tone,  following  the  previous  order  of  adding  tones  by  suc- 
cessive  thirds.      (Sec   Collateral  Reading.   §?.">,    [2]-[3].) 


(iiddcd    Lessons    in    Iltinnoii //  103 

1 1  will  have,  as  a  result  of  this  huildiug,  four  different 
tones,  and  will  therefore  ah^'ays  be  dissonant,  three  differ- 
ent tones  being  the  limit  of  consonant  combinations. 

(3)  Statement.  A  chord  of  the  seventh,  like  the 
triads,  may  be  formed  ujion  each  and  every  note  of  the 
scale.  The  chords  formed  upon  the  different  degrees  will 
differ  in  their  character,  just  as  do  the  various  triads 
of  the  key,  and  for  the  same  reasons:  viz.,  that  the  con- 
stituent intervals  differ.  For  example,  the  chord  of  the 
seventh  upon  the  first  degree  of  the  scale  of  C,  composed 
of  the  tones  C-E-Cl-B,  has  a  Major  third,  a  Perfect  fifth 
and  Major  seventh,  while  the  chord  of  the  seventh  ui)on 
the  second  degree  of  the  same  key  has  a  Minor  third. 
Perfect  fifth  and  Minor  seventh,  otherwise  described  as 
Minor  triad  with  Minor  seventh.  Other  degrees  of  the 
scale  will  exhibit  other  forms,  the  Minor  scale  showing 
some  that  are  extremely  disagreeable  in  their  dissonance. 
This  differing  character  in  the  various  chords  of  the 
seventh  should  not  be  considered  a  defect  in  the  system, 
but  a  great  excellence,  for  differing  characteristics  are 
requisite  in  music  as  in  social  life. 

(4)  Observation.  Some  chords  of  the  seventh,  while 
called  dissonant,  are  still  very  pleasant  to  the  ear.  This 
is  explained  by  the  fact  that  a  dissonance  does  not  neces- 
sarily represent  a  discord,  but  the  quality  of  unrest  or 
incompleteness,  as  shown  in  Collateral  Reading,  %QCi,  (2). 

(5)  Statement.  In  the  following  exercises  only  scale 
tones  should  be  used,  regardless  of  the  effect  or  form  of 
chord  which  results.  These  chords  must  all  be  in  the 
key,  and  this  is  only  possible  when  every  tone  belongs 
to  the  scale. 

(6)  Exercises,  (a)  Taking  in  turn  each  degree  of 
the  scale  of  C  Major  as  a  root,  form  a  chord  of  the 
seventh,  and  describe  as  shown  above  in  (3). 

(b)  Proceed  similarly  in  all  other  Major  keys. 

(c)  Proceed  similarly  in  all  Minor  keys. 


104  Graded   Lessons    ni    Ilarmonij 

LESSON  20. 

CHORDS  OF  THE  SEVENTH  (Cont.) 

Different  Positions  of  the  Chords  of  the  Seventh. 

123.  Note  1.  It  is  thought  best  to  take  the  different  positions 
and  inversions  of  the  triads— or  to  learn  thoroughly  to  con- 
struct the  chords  in  different  forms— before  taking  up  the 
subject  of  the  resolutions.  For  this  reason  we  will  skip  over 
a  few  pages  of  H.  S.,  returning  to  them  after  a  few  lessons. 

Note  2.  As  with  triads,  the  chords  of  the  seventh  may 
appear  in  different  positions;  that  is,  different  notes  may 
appear  in  the  upper  voice.  Positions  are  named  similarly  to 
those  of  the  triads:  position  of  the  third,  position  of  the 
fifth,  position  of  the  seventh  and  position  of  the  octave. 

WRITTEN  EXERCISES. 

Write  the  chord  of  the  Dominant  seventh  upon  G  in 
its  four  positions,  marking  each  one  and  using  two  staves. 

KEYBOARD  EXERCISES. 

Using  two  hands,  play  the  chord  of  the  Dominant  sev- 
enth on  G  in  its  different  positions,  naming  each  position 
as  played.  Proceed  similarly  with  all  other  chords  of  the 
Dominant  seventh,  moving  either  chromatically  through 
the  octave  or  following  the  circle  of  fifths. 

Special  Note.  Be  careful  to  distinguish^  between  the 
Dominant  in  the  key  and  the  Dominant  on  a  given  root ;  for 
example,  the  chord  of  the  Dominant  seventh  in  the  key  of  G 
is  very '  different  from  the  Dominant  seventh  on  G.  The 
Dominant  in  the  kev  of  G  is  D-Ff-A-C,  while  the  Dominant 
on  G  is  G-B-D-F. 

124.  KEYBOARD  EXERCISES. 

It  is  comparatively  easy  to  play  the  different  positions 
of  the  chord  of  the"  Dominant  seventh  when  taken  in 
regular  order.  It  is  more  difficult  to  take  any  required 
position   without   having   previously   played   through   the 


(iradcd   Lessons    in    Ildrnninij  105 

various  positions  of  the  chord.  To  gain  facility  in  this 
department  the  student  should  take  one  position  (for 
example,  the  position  of  the  third),  and  play  every  chord 
of  the  Dominant  seventh  in  this  position  without  having 
previously  played  it  in  its  natural  form  of  1-3-5-7.  This 
exercise  should  be  practiced  by  taking  successive  chords, 
following  the  circle  of  fifths.  Similarly  practice  the 
chord  in  the  position  of  the  fifth;  in  the  octave. 

Note  metronome  speed  attained  in  all  of  the  above 
exercises. 

Spkcial  Note.  If  the  pupil  has  any  difficulty  in  finding  the 
various  positions  of  these  chords,  he  should  first  do  the  above 
exercises  in  writing  before  proceeding  with  the  keyboard  drill. 

Inversions  of  the  Chords  of  the  Seventh. 

125.  As  with  the  triads,  chords  of  the  seventh  are  used 
in  their  various  inversions. 

STUDY  H.  S.,  §172. 

WRITTEN  EXERCISES. 

Write  exercises  as  given  in  H.  S.,  §172. 

KEYBOARD  EXERCISES:  H.  S.,  §172. 

Combining  the  Various  Positions  and  Inversions. 

126.  KEYBOARD  EXERCISES. 

Taking  the  position  of  the  octave,  play  the  chord  of 
the  Dominant  seventh  on  G  in  all  its  different  inversions, 
making  with  the  direct  form,  four  different  forms  of  the 
chord. 

Next,  take  the  chord  in  the  position  of  the  third  and 
play  it  in  all  its  inversions. 

Next,  proceed  in  the  position  of  the  fifth,  then  in  the 
position  of  the  seventh,  taking  all  inversions  with  each 
position. 

Next,  let  us  invert  the  foregoing  process  by  taking 
the  direct  form  (Root  in  the  bass)  and  playing  the  chord 
successively  in   its  different  positions. 

Next,  taking  the  chord  in  the  first  inversion  (with 
third  in  bass)   play  with  this  bass  all  the  dift'erent  posi- 


106  dradcd   Lessons    in    Harmon // 

tions.     Proceed  similarly  with  the  sccoiul  and  third  inver- 
sions. 

Repeat  the  above  with  all  the  chords  of  the  Dominant 
seventh. 

Special  Note.  Advanced  students  in  playing  above  may 
try  to  avoid  doubling  the  third  of  the  chord;  that  is,  when 
the  third  is  in  the  bass,  try  to  omit  it  from  the  upper  parts. 

XoTi:.  The  pupil  should  write  the  above  exercises  complete 
in  one  key. 

127.  KEYBOARD  EXERCISES. 

It  becomes  increasingly  difficult  to  combine  any  re- 
quired inversion  of  the  chord  of  the  seventh  with  any 
required  position  of  the  same.  The  following  exercises 
will  therefore  require  continued  drill,  possibly  for  several 
months,  in  order  to  gain  real  facility. 

(a)  Play  the  chord  of  the  Dominant  seventh  upon 
the  root  D  in  the  first  inversion  and  position  of  the  fifth. 

(b)  Similarly,  play  the  chord  of  the  Dominant  seventh 
on  the  root  D  in  its  second  inversion  and  position  of  the 
third. 

(c)  Similarly,  play  the  same  chord  in  the  third  inver- 
sion and  position  of  the  octave. 

Special  Note.  Remember  that  inversion  relates  to  the 
Bass  (or  left  hand),  while  position  relates  to  the  Soprano  (or 
highest  note  in  the  right  hand).  It  will  therefore  be  less 
confusing  in  the  following  exercises  to  think  first:  "What 
is  the  chord?"  (i.e.,  name  to  yourself  the  notes  required  for 
the  given  chord).  For  example,  if  some  inversion  and  posi- 
tion of  the  chord  upon  the  root  G  is  required,  it  is  well  to 
think  of  the  letters  forming  the  chord  (G-B-D-F)  before 
commencing  to  think  of  the  required  inversion  and  position. 
Next,  think  of  the  required  inversion.  For  example,  taking 
the  same  chord,  the  second  inversion  will  bring  D  as  the 
lowest  (or  left-hand  note).  Next  think  of  the  position. 
"Position  of  the  third"  would  bring  B  as  the  highest  note  in 
the  above  chord.  The  reason  for  the  aliove  is  that  if  the 
student  is  required  to  do  two  or  three  things  at  one  time  he 
will  prnhably  do  none  of  them  well.  It  is  better  to  attack  the 
obstacles  one  at  a  time.     Therefore,  in  placing  ciiords  of  the 


(iiddcd    T.cssoii.s    ill    Iltinnoiii/  t('7 

sfviiilh  in  (lilVcre-iit  in  v  (.T.sii  ins  ami  positions,  we  think  (a) 
•What  are  the  notes  oi  a  cliord?"  (b)  "Which  inversion  ?"' 
(This  places  the  left  hand  in  position.)  (c)  "Which  posi- 
tion?" (This  places  the  highest  note.)  Then  we  proceed  to 
••fill  in"  the  inner  voices. 

128.  KEYBOARD   EXERCISES. 

(a)  Beginning  with  the  chord  of  the  Dominant  sev- 
enth upon  the  root  C  and  proceeding  through  the  circle 
of  fifths,  play  each  chord  in  the  first  inversion  and  the 
position  of  the  fifth. 

(h)  Similarly,  play  through  the  circle  of  the  fifths 
the  chord  of  the  Dominant  seventh  in  the  second  inver- 
sion and  position  of  the  octave. 

(c)  Similarly  combine  the  third  inversion  with  the 
])osition  of  the  fifth. 

(d)  Similarly  combine  all  positions  and  inversions, 
working  through  the  circle  of  fifths. 

XoTK.  Do  not  attempt  to  take  this  complete  drill  at  one 
time,  but  spread  it  over  several  days,  and  continue  through 
a  loiig  period.  Facility  in  the  above  is  one  of  the  most  neces- 
sary lines  of  work  for  those  who  would  attain  real  success  in 
the  use  of  chords. 

\-2\K  gUESTIOXS  n-l."),  Kc\\  pp.  SI,  S.T;  1-12,  Key.  pp. 
!Vi'-02. 

Where  There  Are  Two  Sets  of  Figures  Over  One 
Bass  Note. 

i;}0.  Observe  the  following  points  carefully: 

(1)  See  H.  S.,  §131,  especially  (d)  and  (g). 

(2)  When  no  figures  are  given,  the  Common  Chord 
is  intended.     (H.  S\  §131   [a].) 

(3)  When  following  or  preceding  other  figures,  the 
figures  3-5-8  in  any  combination  arc  used  to  indicate  the 
common  chord  as   shown   in  the   illustration.   H.  S..  §131 

(g). 

(4)  It  should  be  observed  that  some  figures  must  be 
given,  otherwise  the  six-four  chord  would  have  neces- 
sarily continued  for  the  whole  time. 

(5)  Observe  further,  that  instead  of  two  sets  of  fig- 
ures over  one  bass  note,  it  would  be  possible  to  divide  the 


108  Graded   Lessons   in   Ilnrmony 

bass  note  into  two  shorter  notes,  connecting  them  by  a 
tie  and  placing  one  set  of  figures  over  each  note.  This 
would  amount  to  the  same  thing  as  having  two  sets  of 
figures  over  the  one  longer  bass  note ;  and  this  is  really 
what  is  meant  by  the  two  sets  of  figures — two  different 
chords  in  succession  which  chance  to  have  the  same  bass 
note. 

EXERCISES. 

Write  out  in  tlircc  positions  each  of  the  following  exer- 
cises: 

Fig.  5.     A 

(.a)         8        1  (*)  t         3  (c)  3         2 


(G)  2  means  chord  of  the  seventh  (its  third  ini'cr- 
sion).  The  2  is  enough  to  give  a  clue  to  the  whole  chord. 
For  example : 

B 

2 


--m: 


The  figure  2  means  here  the  second  from  F,  which  is 
G.  Now  G  and  F  can  get  into  the  same  chord  only  when 
sion  of  this  chord  is  F-G-B-D.  From  F  to  G  is  a  second, 
there  is  a  chord  of  the  seventh,  G-B-D-F,  and  the  inver- 
shown  by  the  figure  2.  Now  two  successive  letters  like 
F-G  can  only  occur  in  an  inversion  of  a  seventh  chord; 
and  the  upper  one  of  the  two  letters  is  always  the  root 
of  the  chord. 

It  is  the  same  way  when  we  find  two  successive  figures 

as  3  g;  the  note  indicated  by  the  upper  figure  will  be 
the  root  of  the  chord.  This  makes  a  very  short  and  easy 
way  to  find  the  root  of  an  inversion  of  the  chord  of  the 
seventh;  and  after  we  have  the  root  of  any  chord,  it  is 
easy  to  add  the  other  tones.  The  figure  2  really  indicates 
two  successive  letters  since  the  figure  1  is  always  "under- 
stood";  it  is  the  bass  note  itself  and  therefore  requires  no 
figure.  When  the  figure  2  is  given,  the  note  indicated  by 
the  "2"  will  therefore  naturally  be  the  root. 


Graded  Lessons   in    Ilarmoni/  109 

The  figuring  of  chords  is  a  kind  of  musical  shorthand 
writing:  as  much  as  possible  is  omitted,  leaving  just 
enough  to  give  a  clue  to  the  chord. 

COLLATERAL  READING. 

131.  (1)  Positions  and  Inversions  of  Chords  of  the  Sev- 
enth. Statement.  As  with  triads,  the  chords  of  the  sev- 
enth are  used  in  all  positions  and  inversions.  There  will 
necessarily  be  four  different  positions  and  three  inversions 
in  addition  to  the  direct  form,  as  the  chord  contains  four 
tones  and  each  may  become  in  turn  the  highest  or  lowest 
note.  (For  illustration  of  positions  and  inversions,  see 
any  text-book  on  harmony.) 

(2)  Observation.  The  most  important  training  in  the 
whole  study  of  harmony,  the  one  that  holds  the  key  to  all 
use  of  the  knowledge  at  the  keyboard  in  improvising  and 
modulating,  as  well  as  of  all  success  in  later  studies,  is 
that  of  forming  the  chords  of  the  seventh  in  every  key. 
in  ez'ery  position  and  inversion.  He  who  can  do  this  need 
fear  no  diiificulties  to  come. 

(3)  Exercises,  (a)  Taking  in  turn  each  chord  of  the 
seventh  in  the  key  of  C,  place  it  in  all  its  different  posi- 
tions, while  keeping  the  left  hand  on  the  root  note. 

(b)  Similarly  combine  each  position  of  the  al)0ve 
with  every  inversion,  by  keeping  the  right  hand  upon  the 
same  position  of  the  chord  while  forming  the  dift'erent  in- 
versions with  the  left  hand. 

(c)  Proceed  similarly  in  all  Major  and  Minor 
keys.  (In  this  exercise  is  sufficient  material  for  several 
months  of  study.) 

(d)  W^ithout  referring  to  the  keyboard,  recite  the 
chords  of  the  seventh  in  their  different  inversions. 

(e)  Make  thorough  drill  at  the  keyboard  in  form- 
ing quickly  any  required  position  and  inversion  of  any  sev- 
enth chord ;  e.g..  What  is  the  second  inversion  of  the 
chord  of  the  seventh  upon  the  root  E  (in  the  key  of  C)  ? 
To  answer  this,  the  student  should  quickly  plav  the  notes 
B-D-E-G. 

(4)  Important  Observation.  1'hc  student  should  give 
especial  attention  to  forming  and  recognizing  the  chord 
of  the  seventh  which  is  found  upon  the  fifth  degree  (if 
every  scale,  called  the  Dominant,  for  this  is  the  most 
important  and  most  frequently  used  chord  in  music. 


no  Graded   Lessons    in   Harmon  1/ 

LESSON  21. 
CHORDS  OF  THE  SEVENTH  (Cont.) 

Consonance  and  Dissonance  as  a  Principle. 

132.  Note.  This  is  one  of  the  most  important  points  in  the 
study  of  Theory.  Work  slowly  and  go  over  this  part  repeat- 
edlj-,  trying  to  absorb  it  point  by  point. 

STUDY  H.  S.,  §§149-151;  also  Key.  150,  p.  73. 
COLLATERAL  READING,  §137,  (l)-(2). 

Importa.xt  Xote.  By  this  great  principle  we  can  divide 
the  whole  of  the  material  of  music  into  these  two  divisions, 
and  so  simplify  the  theory  of  music  in  a  marvelous  way. 
Since  the  Independent  Chords  are  treated  in  just  as  definite 
(tliough  different)  a  way,  consequently,  when  we  determine 
the  character  of  a  chord,  the  appropriate  treatment  of  that 
chord  will  follow  as  a  matter  of  course. 

Let  us  next  proceed  to  find,  through  analysis  of  cliords, 
how  they  are  to  be  treated.  First,  let  us  make  sure  that  the 
proceeding  is   clear  by  answering  at  this  point : 

(a)  How  many  chords  of  the  Dominant  sevemli  may 
be  found  in  any  one  key  ? 

(b)  Describe  tlie  intervals  required  to  form  a  chord  of  the 
Dominant   seventh. 

133.  STUDY  //.  S.,  §§152-155;  also  Key,  pp.  5l'-53.  and 
153.  page  71. 

COLLATERAL  READING,  §137,  (3)-(l). 

134.  QUESTIONS. 

(1)  State  which  are  '"PrinciiJar"  and  which  arc 
'"Secondary"  chords  of  the  seventh. 

(2)  What  is  the  difference  in  construction  between  a 
chord  of  the  Dominant  seventh  and  a  chord  of  tiie  sev- 
enth upon  the  second  dei^ree  of  the  scale? 


(iiddrd    Lessons    in    Ilnrmoni/  111 

135.  XOTl'. 

It  is  not  necessary  in  the  following  exercises  to  hnd  and 
describe  the  interval  of  the  Minor  seventh,  which  is  present 
in  each  chord,  but  each  Augmented  and  Diminislied  interval 
should  be  found  and  described,  and  the  proper  resolution  indi- 
cated. 

WRITTEN  EXERCISES. 

Describe  each  dissonant  interval  and  tell  how  it  should 
resolve  in  the  following  chords:  D-Fff-A-C;  Bb-D-F-Ab ; 
E-Qt-B-D.  Proceed  similarly  with  other  chords  of  the 
Dominant  seventh,  until  you  can  easily  find  the  dissonant 
intervals. 

KEYBOARD  DRILL. 

Take  in  turn  the  following  chords;  while  holding  down 
the  keys,  find  and  describe  each  dissonant  interval : 
G-B-D-F;  F-A-C-Eb;  A-C«-E-G;  B-DS-FS-A.  Continue 
till  the  dissonant  intervals  are  easily  and  quickly  found. 

The  Principle  of  Tendencies. 

13(5.  STUDY  H.  S.,  §§152-155;  alsc  Key.  pp.  5-!-53  and 
153,  page  74. 

COLLATERAL  READIXC.     Study  carefully  §137,   (3). 

Definition.  The  process  of  passing  from  a  dissonant  to 
a  consonant  interval  is  called  "resolving"  the  dissonant 
interval.  We  can  now  speak  of  resolving  the  following 
intervals. 

WRITTEN  EXERCISES. 

(a)  Write  the  interval  of  a  Diminished  fifth  from 
C  and  let  it  progress,  as  shown  in  //.  .S"..  Fig.  43,  to  the 
nearest  consonant  interval,  which  will  be  a  Major  third. 
Observe  that  each  tone  moves  only  a  half-step  to  the  next 
tone.  Observe  also  that  in  this  jirogression  the  letter 
always  changes;  for  example,  C  goes  upward  a  half-stc]) 
to  Db,  not  to  C*. 

Siniilarlv  write  tlie  Diminishctl  fifth  upon  ("tf  and 
resolve  it  as  above.  Proceed  similarly  \vitli  the  Dimin- 
ished fifth  ui)on  each  (chromatic)  degree  of  the  scale 
and  resolve  it. 


112  Graded   Lessons    in   JIarmotii/ 

(b)  Referring  to  Fig.  42  in  H.  S.,  for  an  illustration, 
write  the  interval  of  an  Augmented  fourth  upon  each 
(chromatic)  degree  of  the  scale  and  resolve  it  to  the 
nearest  consonant  interval,  which  will  be  a  IVIinor  sixth. 
Observe  that  each  voice  moves  only  a  half-step  and  that 
the  letter  should  change  as  in  the  resolution  of  the  Dimin- 
ished fifth. 

KEYBOARD  EXERCISES. 

Repeat  the  foregoing  written  exercises  in  resolving  the 
Diminished  fifth  and  Augmented  fourth  upon  each  chro- 
matic degree  of  the  scale.  When  doing  this  be  sure  to 
name  the  notes  as  they  are  played,  somewhat  after  this 
fashion:  "The  Diminished  fifth  Cf-G  resolves  by  con- 
traction to  D-FS,  which  is  a  Major  third";  The  Aug- 
mented fourth  C-FS  resolves  by  expansion  to  B-G,  which 
is  a  Minor  Sixth." 

COLLATERAL  READING. 

137.  (1)  So  many  of  the  foundation  principles  of  musical 
structure  and  so  much  of  the  practical  use  of  musical 
material  are  involved  in  the  chord  of  the  Dominant  sev- 
enth and  its  derivative  chords,  that  it  may  well  be  de- 
scribed as  the  epitome  of  structural  law.  A  knowledge 
of  these  controlling  principles  opens  the  way  to  a  simple 
and  comprehensive  understanding  of  all  musical  structure 
— a  view  of  the  subject  that  shows  the  symmetry  and  uni- 
versality of  Nature. 

In  a  previous  section  the  structure  of  the  chord  of  the 
seventh  was  discussed.  It  was  there  shown  that  the 
chord  is  formed  from  the  triad  by  the  addition  of  another 
tone,  making  a  chord  of  four  tones  and  consisting  of  alter- 
nate letters.  There  are  seven  chords  of  the  seventh  in 
each  key,  for,  like  the  triads,  one  may  be  formed  upon 
each  note  of  the  scale.  The  constituent  intervals  of  these 
various  chords  of  the  seventh  must  vary  according  to  the 
scale  tones  which  are  used  (for  only  scale  tones  may  be 
used  if  we  would  keep  the  chords  strictly  in  the  key), 
resulting  in  various  forms  or  kinds  of  seventh  chords. 
For  example,  the  chord  upon  the  first  degree  (of  a  Major 
key)  will  be  composed  of  a  Major  triad  and  a  Major 
seventh,  making  a  very  harsh  chord,  while  the  chord  ui)on 
the  second  deirrce  will  have  a  Minor  triad  and  a  Minor 


(iradrd   Le.s.iuus    in    JIarmoini  113 

seventh,  giving  an  entirely  different  character  (but  still 
harsh).  Of  the  chords  of  the  seventh  upon  the  seven 
different  scale  tones,  the  one  upon  the  fifth  degree,  or 
Dominant,  is  found  to  possess  qualities  and  properties 
which  distinguish  it  from  all  others.  To  properly  study 
the  chord,  let  us  review  the  principles  from  which  the  use 
of  the  chord  is  developed.  (See  Collateral  Reading  in 
previous  lessons.) 

(2)  The  Principle  of  Resolution.  All  chords  arc 
divided  into  two  great  classes,  indicating  either  a  state  of 
rest  or  a  state  of  seeking  for  rest.  These  classes  are 
known  as  consonant  and  dissonant,  and  the  process  of 
passing  from  a  dissonant  to  a  consonant  chord  is  called 
"Resolution.''  It  is  a  universal  law  of  music  that  disso- 
nant chords  shall  be  "resolved."  As  all  chords  of  the 
seventh  are  dissonant,  it  will  be  seen  that  all  must  re- 
solve, or  proceed,  to  another  chord  which  shall  be  conso- 
nant. 

(3)  The  Principle  of  Tendencies.  In  the  structure  of 
music  two  kinds  of  tendencies  are  recognized:  (a)  Melo- 
dic Tendencies,  or  the  tendencies  of  certain  tones  of  the 
scale  to  proceed  in  definite  directions,  among  which  we 
will  remind  the  reader  of  the  tendency  of  the  seventh 
degree,  or  Leading  Tone,  to  progress  upward  to  the 
Tonic,  and  of  the  fourth  of  the  scale  to  progress  down- 
ward to  the  third  degree;  and  (b)  Harmonic  Tendencies, 
or  the  tendencies  of  certain  dissonant  intervals  to  progress 
in  definite  directions,  of  which  the  more  important' are  the 
tendency  of  Augmented  intervals  to  resolve  by  further 
expansion  into  a  consonant  interval,  and  the  tendency  of 
a   Diminished  interval  to  resolve  by  further  contraction. 

To  illustrate,  the  interval  p  is  an  Augmented   fourth,  which 
tends  to  resolve  by  further  expansion,  thus,   p         '*T  while  the 

p 
interval  d  is  a  Diminished  fifth  and  resolves  thus, 

(4)  Application  of  these  Principles  to  Chords  of  the 
Seventh.  Chords  are  composite,  being  made  up  of  inter- 
vals, and  the  intervals  are  in  turn  composed  of  scale  tones. 
Now   observe   one   of    the   most    important   principles   of 


114  Graded   Le.s.son.s-    in    TTnrmotii/ 

musical  structure:  when  a  chord  is  dissonant,  it  must  be 
resolved;  and  when  a  dissonant  chord  contains  a  tone 
which  has  a  strong  tendency  either  melodic  (i.e.,  as  a 
scale  tone)  or  harmonic,  the  chord  as  a  whole  will  be 
strongly  influenced  or  even  controlled  by  the  tendencies  of 
its  constituent  intervals  and  tones. 

It  should  be  observed  that  the  tendencies  in  their 
operation  are  largely  confined  to  dissonant  chords,  for  a 
consonant  chord  never  contains  a  dissonant  interval,  and 
is  therefore  never  influenced  by  harmonic  tendencies  (only 
dissonant  intervals  have  harmonic  tendencies),  and  a 
melodic  tendency  alone  is  not  sufficiently  strong  to  seri- 
ously disturb  the  quality  of  rest  in  a  consonant  chord. 
But  when  a  dissonant  chord  has  specific  tendencies  in  its 
constituent  intervals  or  tones,  the  general  inclination  to 
progress,  occasioned  by  the  dissonance,  receives  a  power- 
ful influence  in  some  direction,  or  toward  some  particular 
resolution.  Sometimes  the  inherent  tendencies  of  a  chord 
point  in  different  directions,  in  which  case  the  stronger 
tendency  rules,  while  in  others  all  the  tendencies  agree  to 
force  the  chord  in  one  given  direction,  restricting  the 
chord  to  one,  and  only  one,  natural  resolution. 

(5)  Application  to  the  Chord  of  the  Dominant  Sev- 
enth. If  in  the  light  of  the  above-mentioned  principles 
we  examine  the  various  chords  of  the  seventh  in  the  key, 
we  will  at  once  see  why  the  chord  upon  the  fifth  degree 
is  so  much  more  powerful  than  the  other  chords,  through 
its  inheirent  tendencies,  as  to  be  called  the  Dominant  or 
ruling  chord,  for  it  forces  its  own  individuality  to  the 
front,  pushing  its  way  to  the  key  center  by  insistently  re- 
solving to  the  Tonic  triad.  In  the  accompanying  illustra- 
tion, the  roots  of  the  chords  upon  the  successive  degrees 
of  the  scale  are  shown  by  capital  letters,  and  the  tenden- 
cies of  the  tone,  by  the  lines  at  the  side  of  the  letters, 
indicating  the  direction  of  the  tendency. 

1)/  c  d  e  f,v  g  a 

g  a  b/  c  ^//  ^  ^\. 

e  \  ^  ^  b'  c  d    A 

C  D  E  Fv  G  A  By 

12  3  4  5  6  7 


(iradcd   Lessons    in    Ifarmonjf  115 

Observing  the  tendencies  in  this  illustration,  it  will  be 
seen  that  the  only  chords  having  more  than  one  tendency 
are  those  upon  the  fifth  and  seventh  degrees  of  the  scale. 
It  will  be  shown  later  that  the  chord  upon  the  seventh 
degree  is  considered  and  treated  as  practically  identical 
with  that  upon  the  fifth  degree;  that  is,  as  a  form  of 
Dominant  harmony.  The  chord  upon  the  seventh  degree 
will  therefore  be  ignored  for  the  present,  leaving  the 
chord  upon  the  fifth  degree  as  the  one  chord  in  which 
several  distinct  and  separate  tendencies  unite  in  demand- 
ing a  specific  resolution  of  the  chord. 

The  melodic  tendencies  are  for  the  seventh  of  the 
scale,  B,  to  progress  upward  to  C,  and  for  the  fourth 
of  the  scale,  F,  to  progress  downward  to  E.  The  har- 
monic tendencies  are  that  the  Diminished  fifth,  B-F, 
shall  resolve  by  contraction  to  C-E.  It  should  be  particu- 
larly noted  that  in  this  case  the  same  letters,  B  and  F, 
are  involved  in  both  the  melodic  and  harmonic  tendencies, 
or,  in  other  words,  that  each  tendency  reinforces  the 
others  in  demanding  the  same  resolution.  It  is  not  a 
mere  coincidence  that  this  should  occur  in  this  chord,  for 
it  will  be  shown  that  this  point  is  the  principle  which  pro- 
claims that  the  chords  of  the  Dominant  seventh,  the 
Dominant  Minor  ninth,  the  Diminished  seventh  and  the 
three  forms  of  the  Augmented  sixth  chords,  as  well  as 
the  wonderful  group  of  "Attendant  Chords,"  are  merely 
different  forms  of  one  and  the  same  chord  thought,  with 
similar  origin,  similar  treatment,  and  similar  resolution. 
It  is  further  most  remarkable,  and  sufficient  proof  of  the 
truth  of  the  theory,  that  in  every  position  and  inversion  of 
Dominant  harmony,  and  in  every  one  of  the  above-men- 
tioned forms,  the  "tendencies  are  infallible  in  their  opera- 
tion, no  exceptions  being  found  under  any  conditions.  In 
the  accompanying  illustration  is  shown  the  resolution  of 
the  Dominant  seventh  chord  in  various  forms  to  its  Tonic 
triad.  The  tendencies  are  here  shown  by  the  oblique 
lines. 

"^e  f^  h^  c 

g        g  b^*"^  c  ^^e 


116  Graded   Lessous    in    Ilarmoni/ 

Those  letters  which  have  no  lines,  since  they  are  not 
tendency  notes,  may  be  called  neutral  tones,  and  are  free 
to  progress  either  upward  or  downward  to  a  place  in  the 
chord  of  resolution,  or  to  retain  the  same  note,  as  may  be 
found  desirable. 


(Irudid   Lessons    in    llaimunfi  117 


LESSON  22. 

CHORDS  OF    IHK  SEVENTH  (Cont.) 

The  Principle  of  Resolution. 

138.  In  past  lessons  we  have  learned  that  chords  are  com- 
posed of  intervals  and  that  intervals  give  quality  to  the 
chords.  We  learned  further  that  chords  composed  exclu- 
sively of  consonant  intervals  are  consonant  and  require 
no  resolution ;  while  chords  containing  even  one  dissonant 
interval  must  be  classed  as  dissonant  chords,  requiring  to 
l)e  resolved.  We  have  learned  also  that  dissonant  inter- 
vals have  a  natural  tendency  toward  some  particular  reso- 
lution, described  under  the  head  of  ''Harmonic  Ten- 
dencies." 

It  is  only  a  logical  deduction  from  the  above  to  the 
statement  that  if  the  dissonant  interval  or  intervals  in  a 
chord  are  resolved  according  to  their  natural  tendencies, 
the  chord  will  be  resolved  in  the  most  natural  manner. 
Let  us  apply  this  to  the  resolution  of  the  chord  of  the 
Dominant  seventh  by  studying  carefully  H.  S.,  §§155-159, 
and  Key,  157-159,  including  all  the  keyboard  and  written 
exercises  given. 

Re-Statement  of  the  Foregoing  as  a  Principle. 

139.  Dependent  chords  (all  chords  of  the  seventh  are  de- 
pendent chords),  contrary  to  the  methods  universally 
taught,  are  not  treated  in  a  haphazard  or  chance  way,  but 
follow  well  defined  and  perfectly  natural  principles,  which 
are  practically  universal  in  their  application.  This  treat- 
ment is  the  direct  outcome  of  the  natural  qualities  of  the 
chord  tones  themselves.  By  "qualities"  is  meant  certain 
tendencies  which  are  inherent  in  various  scale  tones. 
These  tendencies  are  less  pronounced  in  consonant  or  inde- 
pendent chords,  but  are  developed  or  brought  into  activity 
by  the  presence  of  dissonance. 


118  drtulcd    Lessons    in    Ila rnioii  1/ 

Resolution  of  Inversions  of  the  Chords  of  the 
Seventh. 

STUDY  //.  S.,  §17;J,  and  Collateral  Reading,  §142. 
EXERCISES:  H.  5-.,  §173. 
KEYBOARD  EXERCISES. 

(a)  Take  the  chord  of  the  Dominant  seventh  on  the 
root  G,  place  it  in  turn  in  all  positions  and  inversions,  and 
resolve  each  as  shown  in  H.  S.,  §§172-173. 

(b)  Take  in  turn  every  other  Dominant  seventh  chord 
and  treat  as  above. 

140.  EAR-TRAINING. 

Try  to  contrast  triads  with  chords  of  the  seventh, 
noting'  the  incomplete  effect  of  the  latter  and  the  restful 
quality  of  the  former.  When  working  with  the  different 
inversions  and  positions  of  the  chords  of  the  seventh, 
listen  to  the  dissonant  element  of  the  Augmented  fourth 
or  Diminished  fifth  and  try  to  feel  the  direction  in  which 
these  voices  tend  to  progress.  This  will  help  to  deter- 
mine the  inversion  or  position. 

Practical  Application  of  the  Chords  of  the  Dominant 
Seventh. 

141.  Having  learned  to  construct  the  chords  of  the  Domi- 
nant seventh  in  all  keys  and  to  resolve  them,  we  should 
now  learn  to  put  our  knowledge  into  practical  use  as 
follows. 

Cadences. 
STUDY  H.  S.,  §190. 

WRITTEN  EXERCISES. 

(a)  Write  the  cadences  in  six  IMajor  and  six  Minor 
keys  as  shown  in  (a)  H.  S.,  Fig.  60. 

N.B.  If  found  at  all  difficult,  the  above  should  be  done 
in  twelve  ^lajor  and  IMinor  keys. 

(b)  Form  a  perfect  cadence  in  which  the  Leading 
Tone  of  the  scale  is  in  the  Soprano  of  the  first  (or  Domi- 
iiant  seventh)   chord. 

Note.  After  writing  one  or  two  examples  of  exercises 
(b)  read  H.  S.,  §164.  Perform  this  exercise  in  six  Major  and 
six  Minor  keys  not  using  the  .same  keys  as  in  exercises  (a) 
unless  exercise   (a)   was  written  in  all  keys. 


(Iradctl    Lessons    in    Utirnidui/  119 

(c)  Write  examples  of  imperfect  cadences,  not  neces- 
sarily like  (b)  in  Fig.  60,  //.  S..  but  make  as  many  differ- 
ent forms  as  you  can. 

(d)  Write  plagal  cadences  as  illustrated  in  (c),  //.  S., 
Fig.  GO,  in  three  Major  and  three  Minor  keys.  Place  the 
chord  in  as  many  positions  as  possible.  Observe  that  the 
"amens"  sung  at  the  close  of  hymn  tunes  are  usually  only 
plagal  cadences. 

KEYBOARD  EXERCISES. 

Repeat  the  above  exercises  in  every  Major  and  Minor 
key,  in  as  many  different  positions  and  inversions  as 
possible. 

Note.  The  third  and  seventh  of  the  Dominant  seventh 
chord  are  called  "tendency  notes"  or  "active  notes."  the  pro- 
gressions of  whicli  are  fixed.  The  other  two  notes  (first  and 
fifth  of  the  Dominant  seventh  chord)  have  no  tendencies— 
therefore  we  call  them  "neutral,"  or  inactive  tones — and  they 
have  no  fixed  progression,  but  may  progress  either  upward  or 
downward,  or  may  remain  quiet,  whichever  will  produce  the 
best  effect.  If  the  fifth  were  to  go  upward  in  the  resolution, 
it  would  double  the  third  of  the  chord  :  since  it  is  better  to 
double  tlie  Root  of  a  chord  rather  than  the  third,  the  fifth 
usually  progresses  downward  in  the  resolution. 

COLLATERAL  READING. 

142.  (1)  In  summing  up  the  matter,  we  find  that  the  chord 
of  the  Dominant  seventh  has  an  almost  irresistible  in- 
clination to  resolve  to  the  Tonic  of  the  key,  not  because 
one  is  the  Dominant  and  the  other  the  Tonic,  but  because 
the  Dominant  chord  contains  within  itself  melodic  and 
harmonic  tendencies  which  unite  to  compel  the  chord  to 
progress  in  that  direction.  We  are  now  better  enabled  to 
see  the  full  meaning  of  the  statement  that  a  "chord  is  com- 
posite, being  made  up  of  intervals,"  and  to  realize  that 
the  character  and  qualities  of  the  intervals  go  far  toward 
determining  the  quality  and  treatment  of  the  chord. 

(2)  It  would  be  a  pleasant  digression,  at  this  point, 
to  show  how  the  standard  theorists  of  the  past  in  their 
teachings  and  writings,  have  unconsciously  followed  the 
principle  of  tendencies  without  being  able  to  formulate  the 
subject.  Practically  all  the  rules  of  part-writing  are 
founded  on  the  cooperation  or  the  opposition  of  these  ten- 
dencies and  other  simple  influences;  the  opposition  of  these 


120  Graded    Lt'ssoiia    in    Jlarmoii  1/ 

tendencies  explains  in  a  wonderfully  simple  manner,  the 
numerous  so-called  exceptions  to  the  rules  of  harmony, 
which  may  be  shown  not  to  be  exceptions  or  imperfections 
in  any  sense  of  the  word.  Further,  the  study  of  tenden- 
cies, harmonic  and  melodic,  will  reveal  why  certain  pro- 
gressions and  certain  melodies  are  sometimes  awkward 
and  unsatisfactory  when  they  cannot  be  called  incorrect. 
In  a  word,  the  study  of  the  subject  from  the  point  of  view 
here  described  will  take  one  to  the  very  heart  of  music, 
putting  reason  and  principle  in  the  place  of  instinct.  Dr. 
Jadassohn  used  to  say,  "If  you  will  w-ork  very  hard  for 
many  years,  you  will  eventually  feel  why  one  note  must 
pass  up  and  another  down.  I  cannot  tell  you  in  words." 
The  doctor  felt  but  did  not  knoiv  the  inner  principles  of 
tendencies,  which  are  able  to  explain  the  subtlest  shadings 
of  meanings  in  music.  In  this  subject  there  is  material 
for  the  most  serious  study  by  any  musician,  sufficient  to 
occupy  many  months,  and  rich  in  the  reward  for  earnest 
thought. 

This  exposition  of  what  is  believed  to  be  the  most 
important  single  feature  of  musical  theory  is  necessarily 
brief  and  lacking  in  detail,  but  the  interested  student  will 
be  able  experimentally  to  test  the  principles  involved 
through  the  following  exercises,  or  by  reference  to  H.  S. 

(3)  Exercises,  (a)  Form  chords  of  the  Dominant 
seventh  in  all  keys,  both  at  the  keyboard  and  in  writing ; 
trace  out  the  tendency  notes  and  intervals  and  resolve. 

(b)   Repeat  in  all  positions  and  inversions. 

143.  QUESTIONS. 

When  you  have  thoroughly  studied  Lessons  19-22,  write 
answers  to  all  the  questions  in  Key,  pp.  81,  83-86.  Also 
rewrite  answ^ers  to  those  on  pp.  91-92.  This  will  reveal 
the  weak  spots. 

144.  ANSWER  TO  QUESTION  21,  Key,  p.  83. 

This  point  is  a  development  of  the  order  of  sharps  or 
flats  in  a  signature.  If  we  remember  that  in  a  signature 
or  scale  the  sharps  or  flats  ahvays  enter  in  a  prescribed 
order,  and  that  the  presence  of  the  second  sharp  or  flat 
always  presupposes  (in  fact,  requires)  the  presence  of  the 
first,  we  can  find  a  simple  and  conclusive  way  of  deter- 
mining the  key  from  this  chord  alone. 


Graded    Le.s.soiis    in    Uannonji  121 

Let  us  take  any  chord  of  the  Dominant  seventh,  for 
example,  G-B-D-F.  Now  the  first  sharp  to  appear  m  a 
key  is  F«,  but  as  we  here  have  F,  it  shows  that  the  key  to 
which  this  chord  belongs  has  not  even  one  sharp  (smce,  if 
it  had  anv  sharps  whatever,  F  could  not  be  natural). 
I'urther,  since  in  the  order  of  flats  Bb  is  the  first,  the  tact 
that  we  here  have  B^  shows  that  this  chord  belongs  to  a 
kev  which  has  not  even  one  flat. 

'Now  what  key  has  not  even  one  flat  or  sharp?  ine 
answer  is  C,  and  this  chord,  G-B-D-F,  therefore  belongs 
to  the  key  of  C  alone.  . 

Illustration.  E-GJ-B-D.  The  Gtf  shows  that  this 
-  chord  belongs  to  a  key  having  at  least  three  sharps,  since 
GJf  in  a  signature  implies  the  presence  of  F#  and  CJf.  1  he 
Dtl  shows  that  the  key  could  not  have  four  sharps,  since 
D  would  be  that  fourth  sharp.  Now  what  key  has  three 
sharps  but  not  four?     Ans.  A.  ,,      ,• 

You  will  observe  that  the  "sharpest'  note  (leading 
tone)  and  the  "flattest"  note  (fourth  of  the  scale)  are 
the  significant  notes. 

Read  H.  S.,  §§29,  250. 
NOTE  OX  QUESTION  36,  Key,  p.  84. 

I  think  of  Augmented  and  Diminished  intervals  as  the 
"extreme"  forms  of  dissonance,  and  I  think  of  Major  and 
Minor  intervals  (when  dissonant  at  all)  as  "milder' 
forms  The  above  is  like  thinking  of  Soprano  and  Bass 
as  the  "outer"  parts  and  the  Tenor  and  AUo  as  "inner 
parts.  This  will  appeal  to  the  thinking  musician,  if  he 
considers  the  perfect  interval  as  the  one  most  closely  ap- 
proximating the  scientifically  estimated  interval,  whde  the 
Major  form  is  a  trifle  larger  than  what  science  would 
require  and  the  Minor  a  trifle  smaller. 

V'Augmented 

Shown  in  tabulated  form  it     f  /^pgrfect the  center. 

would  be  somewhat  like  this:        V^Minor 

^Diminished 

With  the  above  for  a  preliminary,  which  the  student 
may  forget  if  it  does  not  appeal  to  him  (I  can  make  no 
further  explanation,  since  the  point  is  only  a  theory  or 
phantasy  of  my  own),  we  may  make  this  statement: 


122  (traded    Lessons    in    Ilarmoni/ 

In  the  resolution  of  dissonances,  it  will  be  found  that 
in  the  '"extreme"  forms  both  tones  progress;  while  in  the 
"milder"  or  "moderate"  forms  it  is  sufficient  if  only  one 
tone  progresses.  Applying  this  to  the  resolution  of  the 
Dominant  seventh  chord,  it  will  be  noted  that  in  the  inter- 
val of  the  Dim.  fifth  or  Aug.  fourth  both  tones  must  pro- 
gress, while  in  the  same  chord  the  interval  of  the  Minor 
seventh  requires  that  only  one  tone  progress. 

Think  this  over — you  may  be  interested. 

ANSWER  TO  QUESTION  11,  Key,  p.  92. 
First  inversion. 

ANSWER  TO  QUESTION  12,  Key,  p.  D2. 

In  every  inversion  there  will  be  consecutive  figures  or 
notes  upon  successive  degrees ;  the  upper  one  of  these  two 
is  alwavs  the  root. 


Graded    Lessons    in    Ilttrrnoii  i/ 


123 


LESSON  23. 

CHORD  OF  THE  SEVENTH  (Cont.) 

The  Closing  Formula. 

145.  This  is  a  most  useful  drill  for  every  student,  as  it  can 
at  first  be  given  in  exceedingly  simple  form  and  afterward 
elaborated  until  it  becomes  very  effective  for  improvisation. 

STUDY  H.S.,  §191;  also  Key,  191. 
Illustrations  of  a  closing  formula. 

Fig.  5. 


(<:) 


'5> 


"2? 


V7 


The  student  should 
write  and  play  all 
these  forms  in  their 
///ree  positions. 


WRITTEN  EXERCISES. 

Write  in  four  Major  keys  the  closing  formula  as  shown 
in  Fig.  5;  (a)  above.  (Advanced  students  may  also  per- 
form the  exercises  in  the  Minor  keys.) 

KEYBOARD  EXERCISES. 

Following  the  same  form,  play  the  closing  formula  in 
everv  Major  kev. 


124 


(haded    Lessons    in    llarmonji 


A     FEW      EXAiMPLES    OF    CLOSING     FORMULA 
WITH  INVERSIONS. 

Fig.  6.     A 

This  is  not  a  complete 
ending,  since  it  is  not  a 
"perfect  cadence." 


It  might  be  completed  by 
the  addition  of  another  closing 
formula. 


Three  parts  with  Passing  Notes. 
,FiG.  7. 


14(5.  Try  to  form  examples  in  the  same  or  other  keys, 
more  or' less  after  the  above  order.  If  yoti  find  difficulty, 
try  to  transpose  these  into  other  keys.  This  will  give 
some  help. 

Note.  The  cliords  may  be  introduced  in  any  order,  simply 
remembering  to  use  Vt  just  before  the  final  Tonic  chord. 

Important  Note.  In  playing  the  closing  formula,  it  is 
essentia]  that  the  final  chord  should  fall  upon  a  strong  beat, 
usually  the  first  beat  of  the  measure,  and  the  ne.xt  preceding 
chord— the  Dominant  seventh— should  appear  upon  (or  at 
least  continue  through)  the  last  beat  of  tlie  preceding  measure. 


(iradcd   Lessons   in    Ilarmoni/  125 

147.  WRIT  TEX  EXERCISES. 

Following  illustration  (b),  Fig.  5  above,  write  the 
closing  formula  in  four  Major  keys.  (Advanced  students 
will  do  the  same  in  the  Minor  keys.)  (N.B.  Do  not  use 
the  same  keys  as  in  the  previous  written  exercise.) 

KEYBOARD  EXERCISES. 

Following  the  above  form,  play  the  closing  formula  in 
all  Major  keys. 

148.  WRITTEN  EXERCISES. 

Following  the  illustration  (c),  F"ig.  5,  write  the  closing 
formula  in  four  Major  keys.  (Advanced  students  will  do 
the  same  in  the  Minor  keys.) 

KEYBOARD  EXERCISES. 

Following  the  above  form,  play  the  closing  formula 
in  all  Major  keys. 

149.  KEYBOARD  EXERCISES. 

The  student  should  play  both  the  cadences  and  the 
various  forms  of  the  closing  formula  in  the  form  of 
"Bounding"  and  "Rocking"  chords.  An  illustration  of  the 
"Bounding"  chords,  and  also  of  the  "Rocking"  chords  as 
played  by  the  student  should  be  written  out  complete  in 
one  key  as  part  of  this  lesson. 

150.  QUESTIONS  1-17,  Key,  pp.  114-115. 


120  Graded   Lessons    in   Jlarmoiu/ 


LESSON  24. 

PART-WRITING— DOM.  SEVENTH  CHORD. 

The  Principles  of  Part-Writing. 

l.-jl.  In  previous  lessons  on  part-writing,  repeated  allusion 
has  been  made  to  the  principles  described  in  H.  S.,  §§161- 
109:  and  Key,  pp.  64-67. 

STUDY  with  great  care  H.  S.,  §§101-169,  and  Key, 
pp.  64-67.  Do  not  leave  it  till  every  point  has  been 
thoroughly  considered.  This  matter  should  be  frequently 
read  over  and  kept  in  mind  ivhilc  doing  the  zvork  in  part- 
Zi'riting.  Beyond  this  it  is  difficult  to  give  any  further 
specific  rules  for  guidance  in  the  study  of  part-writing; 
in  the  last  analysis  it  will  be  found  that  tact  and  musical 
feeling  are  of  far  greater  importance  than  these  com- 
paratively elementary  rules. 

EXERCISES  IN  PART-WRITING. 

H.  S.,  §160  and  §170,   3  ex.     Do  not  write  more  till 
you  can  write  these  correctly  without  help  from  the  Key. 

COLLATERAL  READING. 

152.  (1)  Statement.  It  should  be  observed  that  the  qual- 
ity of  dissonance  is  the  first  element  of  the  principle  of 
resolution.  The  unrest  of  the  interval  is  shown  in  the 
incompleteness  of  the  chord,  forcing  it  to  i)rogrcss  to  a 
consonant  chord. 

(2)  Statement.  As  tlie  presence  of  the  dissonance 
is  the  force  which  causes  the  chord  to  progress,  so  the 
specific  quality  of  the  interval  determines  what  that  move- 
ment shall  be,  or,  in  other  words,  determines  the  resolution. 
This  fact  is  believed  to  be  the  most  vital  element  in  the 
study  of  theory,  the  one  with  the  widest  application,  and 
unfortunately,  the  one  most  neglected.  It  is  shown  in 
the  following : 


Graded  Lessons   in    Ilarmoni/  127 

PRLXCIPLE  OF  HARMONIC  TEXDEXCIES. 

(3)  Statement.  The  most  prominent  quality  of  a  dis- 
sonant interval,  after  its  quality  of  dissonance,  is  the 
unrest  or  incomplete  effect,  and  the  tendency,  through 
this  unrest,  to  progress  in  certain  definite  directions. 

(4)  Statement.  As  compared  with  the  normal  form, 
the  Augmented  form  is  an  expression  of  a  size  abnor- 
mally large,  and  has  a  natural  tendency  toward  further 
expansion  into  some  other  and  larger  interval,  rather  than 
to  retreat  to  its  normal  form.  (See  H.  S.,  §154).  Simi- 
larly, the  Diminished  interval  is  an  expression  of  abnor- 
mal smallness,  and  tends  toward  development  by  contrac- 
tion into  another  and  smaller  interval.  Formally  stated: 
(1)  Augmented  intervals  tend  toward  further  expansion; 
and  (2)  Diminished  intervals  tend  toward  further  con- 
traction. E.g.,  the  Augmented  fourth,  F-B  (play  it), 
tends  to  expand  to  E-C :  while  the  Diminished  fifth,  B-F 
(play  it),  tends  to  contract  to  C-E.  The  demand  for  ex- 
pansion or  contraction  does  not  necessarily  exact  a  move- 
ment of  both  tones  of  the  interval,  though  it  frequently 
does.  See  H.  S.,  §68.  (N.B.  It  will  be  well  to  do  again 
the  additional  exercises  in  Key,  p.  17.) 

(5)  Statement.  In  addition  to  the  tendencies  of  Aug- 
mented and  Diminished  intervals  shown  in  the  preceding 
statement,  there  are  also  tendencies  on  the  part  of  the 
dissonant  Major  and  ]\Iinor  intervals.  (The  only  disso- 
nant Major  and  Minor  intervals  are  the  seconds  and 
sevenths.)  Of  these  the  Major,  representing  the  larger 
form,  tends  to  resolve  by  further  expansion,  while  the 
Minor,  or  smaller  form  tends  toward  further  contraction. 
I'-or  example,  play  the  Minor  seventh,  C-Bb,  when  it  will 
be  seen  to  tend  toward  the  interval  C-A  or  Db-Bb,  resolv- 
ing by  contraction.  Xow  play  the  Major  second  Bb-C, 
when  it  will  be  seen  to  tend  toward  A-C  or  Bb-Db,  resolv- 
ing by  expansion. 

(6)  Deduction.  A  very  simple  and  natural  deduction 
may  be  drawm  from  (4)'- (5)  above,  which  assists  in 
placing  the  subject  before  us  in  a  logical  and  practical 
form.  Observing  the  table  in  §66,  (1),  it  will  be  noted 
that  while  Major  and  Minor  are  correlative  as  are  also 
Augmented  and  Diminished,  the  Perfect  stands  by  itself, 
in  the  apparent  center  between  Major  and  Minor. 
Further,   the  Perfect  interval  is  the  one  interval  which 


128  dradcd   Lessons    in    Harmonii 

is  never  dissonant,  and  therefore  is  not  subject  to  the  law 
of  harmonic  tendencies.  It  is  but  a  simple  deduction 
from  these  facts  to  consider  the  Perfect  as  the  central 
form,  dividing  the  two  larger  intervals,  Major  and  Aug- 
mented, from  the  two  smaller  intervals,  the  jNIinor  and 
Diminished.  Further,  observe  that  those  dissonant  inter- 
vals which  are  larger  than  Perfect  resolve  by  expansion, 
while  those  which  are  smaller  than  Perfect  resolve  by 
further  contraction.  Formally  stated,  the  principle  of 
harmonic  tendencies  is  as  follows.  (1)  All  dissonant 
intervals  are  subject  to  the  laws  of  harmonic  tendencies, 
tending  either  toward  expansion  or  contraction  in  their 
resolution.  (2)  Of  these  dissonant  intervals,  the  Major 
and  Augmented  forms  have  a  natural  tendency  toward 
resolution  by  further  expansion,  while  the  INIinor  and 
Diminished  intervals  tend  toward  resolution  by  further 
contraction.  Remember  that  only  dissonant  intervals 
possess  harmonic  tendencies.  Further,  these  tendencies 
are  found  to  be  inherent  in  the  intervals  themselves,  like 
the  melodic  tendencies  of  scale  tones,  and  not  artificially 
added.  Examples  of  various  dissonant  intervals  are  given 
below,  with  dashes  affixed,  indicating  the  natural  progres- 
sions of  the  tones  composing  the  intervals,  w'hether 
upward,  horizontal  or  downward,  in  progression  to  conso- 
nant intervals : 

F^  ^c  ^^f  F^^    -  -  f 

^^e  B^^  E'^      -  -  e  ^e 

or  or  f 

^c  Fv^  F f  / 

B--^  ^e  ^^  E--e^ 

Dim.  5th         Aug.  4tli  Maj.  7tli  Min.  2n(l 

(7)  Observation.  Xote  that  in  the  extreme  forms — 
Diminished  and  Augmented^both  notes  of  the  interval 
progress,  while  in  the  less  extreme  forms — Major  and 
Minor— it  is  sufficient  if  one  note  progresses  while  the 
other  remains  stationary. 

(8)  Exercises,  (a)  Form  examples  of  all  the  disso- 
nant intervals  mentioned  in  §66,  (1),  indicating  the  normal 
progression  of  each  tone,  as  shown  in  (-l)-(5)   above. 


Graded  Lessons   in   Ilarmoni/  129 

(b)  Examine  the  following  chords,  finding  the  dis- 
■sonant  intervals  and  indicating  the  proper  progression  of 
each  tone:  G-B-D-F;  A-C$-E-G;  B-D-F-Ab ;   G#-B-D-F. 

(c)  Examine  similarly  dissonant  chords  in  printed 
music. 


130  Graded   Lessons    in   II armunij 


LESSON  25. 

PART-WRITING— DOMINANT  SEVENTH 

CHORD  (Cont.) 

Special  Directions,  Hints,  Etc. 

153.  You  have  now  had  sufficient  experience  in  part- 
writing  to  reahze  that  it  is  not  a  matter  of  absolute  and  in- 
flexible rules  which  always  operate  in  the  same  way,  but 
you  now  begin  to  find  that  what  is  good  in  one  place  may 
not  be  desirable  or  even  correct  in  another.  You  also  are 
wishing  to  learn  by  what  authority  your  teacher  objects  to 
a  progression  at  one  time  while  allowing  it  at  another.  I 
beg  you  to  believe  that  it  is  not  a  mere  whim  or  a  desire 
to  use  the  red  pen.  Dr.  Jadassohn  used  to  say  that  these 
things  cannot  be  taught,  but  if  the  student  lived  long 
enough,  practiced  part-writing  regularly,  and  had  a  musi- 
cal disposition,  he  might  ultimately  learn  to  feci  that 
which  could  not  be  expressed  in  words.  Now  I  am  in- 
clined to  take  issue  with  him,  to  a  certain  extent  at  least, 
for  I  believe  the  earnest  student  can  learn  to  know  defi- 
nitely when  a  progression  is  acceptable  and  when  it  is  not 
suited  to  the  occasion. 

PART-WRITIXG  is  a  matter  of  judgment,  of  recon- 
ciling apparently  opposing  rules;  but  the  judgment  should 
rest  upon  a  consideration  of  the  nature  of  the  material 
employed  and  the  objects  to  be  attained.  It  may  be  said 
in  passing  that  -many  of  the  older  rules  of  part-writing 
appear  to  have  been  formulated  with  reference  to  only 
the  most  conventional  progressions ;  and  when  other  con- 
ditions arise,  it  will  l^e  found  that  these  rules  (which 
are  mostly  prohibitions)  fail  to  apply.  Further,  it  may  be 
said  that  many  rules  (such  as  the  one  regarding  the  re- 
tention of  a  "common  note"  in  the  same  voice)  are  de- 
signed merely  to  guide  the  first  attempts  of  the  student, 
the  rules  being  reduced  to  the  rank  of  suggestions  without 
obligation  when  the  student  is  more  experienced;  or  they 
may  be  considered  as  crutches,  to  be  laid  aside  at  the 
proper  time.     For  these  reasons  the  student,  as  he   ad- 


Graded   Lessons    in    Harmon  tf  131 

vances,  should  not  be  surprised  to  sec  progressions  per- 
mitted or  demanded,  which  at  first  were  forbidden. 

The  basis  for  correct  judgment  is  found,  first,  in  the 
nature  of  the  material  employed.  By  this  is  meant  that 
there  are  (a)  individual  qualities  inherent  in  the  different 
degrees  of  the  scale  out  of  which  grows  the  principle  of 
Melodic  Tendencies;  and  (b)  the  result  of  combining 
tones  into  intervals,  out  of  which  grows  the  principle  of 
Harmonic  Tendencies;  and  (c)  the  Suggestive  Qualities, 
various  items  outlined  in  H.  S.,  §161,  (4) -(8). 

To  illustrate  the  thought  in  (a)  and  (b)  above,  it  will 
suffice  to  say  that  a  hidden  fifth  would  be  wrong  if  so 
Ijlaced  in  the  scale  that  the  melodic  tendency  of  some 
important  note  would  be  violated,  while  a  similar  progress 
in  another  part  of  the  scale,  where  the  tendencies  were 
not  violated  would  be  permitted. 

STUDY. 

The  student  will  now  study  again  H.  S.,  §§101-109; 
also  Key,  pp.  6-4-67,  noting  particularly  that  this  recon- 
ciling of  opposing  influences  is  much  like  the  exercise  of 
tact  in  every-day  life ;  it  is  much  easier  to  use  tact  than  to 
force  our  way,  regardless  of  others.  So  remember  that 
the  early  rules  of  part-writing  are  much  like  the  rules  of 
childhood,  to  be  replaced  later  by  maturer  judgment. 

EXERCISES  IX  PART-WRITIXG. 

Write  the  remaining  exercises  from  the  given  Basses 
in  H.  S.,  §170. 

COLLATERAL  READING. 

I.-.4.  THE   FUXCTIOX   Ol-    TlllC   I'.AR    1 X    Tllb.OUV. 

Perception  of  Music  Through  Hearing. 

(T)  It  is  a  very  limited  method  which  confines  the 
study  to  part-writing.  The  power  to  construct  and  use 
chords  at  the  keyboard,  and  to  recognize  the  structure  of 
music  from  hearing  it.  are  among  the  most  useful  and 
enjoyable  features  of  Theory  study.  More  of  cultivation 
and  musicianship  for  teacher  and  student  may  be  attained 
by  a  short  course  along  these  lines  than  by  years  of 
part -writing.     It    is    difficult    to    give    detailed    directions 


132  Graded   Lessons    in    Harmoni/ 

m  a  limited  space  for  proper  training  in  the  art  of  listen- 
ing intelligently.  The  study  should  be  pursued  upon  the 
basis  of  relationship  (see  Collateral  Reading,  §12,  [1].) 
and  one  may  profitably  follow  several  lines,  as  for 
example : 

(a)  Learning  to  listen  accurately  and  intelligently  to 
the  tones  produced  in  playing.  In  this  respect  the  violin- 
ist and  singer  have  an  advantage  over  the  pianist,  for  they 
must  critically  form  each  tone,  whereas  the  pianist,  having 
the  tones  ''ready-made,"  is  not  obliged  to  concentrate  his 
attention  upon  this  point.  He  must  therefore  be  educated 
to  do  so,  not  only  in  his  daily  study,  but  also  in  listening 
to  the  performances  of  others. 

(b)  Learning  to  write  from  dictation  ])y  means  of  a 
carefully  graded  course  in  musical  dictation.  This  should 
cover  the  power  to  distinguish  between  whole  and  half- 
steps,  the  scales,  intervals,  chords  of  all  kinds,  resolutions, 
connections,  melody,  rhythm,  modulation  and  the  orna- 
ments of  music.  Detailed  directions  may  be  found  in 
H.  S.  A  most  practical  form  of  dictation  and  ear-train- 
ing may  be  given  in  class  or  club  work  by  having  the 
members  follow  with  the  fingers  upon  a  duml)  keyboard, 
or  printed  representation  of  the  keyboard,  the  scale  notes, 
intervals  and  chords  sounded  upon  an  instrument  by  the 
leader.  In  addition  to  the  mental  pictures  formed  from 
hearing,  the  ability  to  produce  is  thus  gained  by  having 
the  fingers  in  that  position  upon  the  keys  in  which  the 
effect  was  originally  produced.  This  association  of  cause 
and  effect  is  of  the  highest  value.  The  use  of  such  a 
representation  of  the  keyboard  in  the  classroom,  by 
which  a  larger  number  may  also  have  the  same  training 
and  actual  drill  as  the  individual  student  at  the  keyboard, 
is  one  of  the  latest  advances  in  Theory  teaching. 

(c)  Trying  to  think  and  sing  certain  intervals;  e.g., 
sounding  C  upon  the  keyboard,  try  to  think  how  far  to 
the  tone  1"  and  test  by  reference  to  the  keyboard.  Later 
extend  this  to  include  all  possible  intervals. 

(d)  Trying  to  think  how  unfamiliar  passages  of 
printed  music  would  sound ;  in  other  words,  mentally  read- 
ing music. 

fc)  Trying  to  achieve  al)Solute  lutch.  Discover  the 
])itch  of  voices,  bells  and  whistles;  also,  think  a  given 
jiilrh,   sing  it,  and   llien   provi'  by  reference    Id  lbc   piano. 


(Ira fled    Lessons    in    ffarmoni/  133 

For  example,  as  yon  read  this,  fix  in  your  mind  and  voice 
the  pitch  of  the  tone  G,  as  nearly  as  you  can,  and  prove 
it  at  the  instrument;  similarly,  try  to  find  the  key  of 
selections  heard  in  the  concert-room. 

(f)   Constantly   noting   the   effect   of   IMajor    and 
Minor  in  keys,  chords,  intervals  and  melodies. 

(2)  At  first,  in  listening,  as  in  early  experiences  with 
a  foreign  language,  only  single  stray  bits  will  be  recog- 
nized, like  a  cadence  in  melody  or  harmony,  or  a  charac- 
teristic rhythmic  feature.  Continued  striving  will  in- 
crease the  capacity,  until  the  ability  may  be  achieved  to 
recognize  successive  chords,  to  follow  a  melody,  to  trace 
modulations,  and  to  have  an  understanding  of  musical 
form;  or  even,  with  the  talented  few,  to  mentally  picture 
the  appearance  of  a  composition  as  it  looks  on  the  score. 


134  Graded   Lessons    in   Ilarmonij 


LESSON  26. 

PART-WRITING— DOMINANT  SEVENTH 
CHORD  (Cont.) 

155.  SPECIAL  NOTE. 

Further  rules  are  not  necessary  in  taking  up  the  study  of 
part-writing  with  inversions.  Remember  the  principles  of 
Tendencies  and  .Individuality  of  Scale  Tones,  and  the  natural 
or  conventional  progressions  of  single  tones  and  chords. 

Students  frequently  misunderstand  the  figuring  of  Basses. 
Read  everything  written  up  to  this  point  about  figuring  of  the 
chords,  and  also  H.  S.,  §199. 

PART-WRITIXG :  H.  S.,  §173. 

156.  EAR-TRAINING. 

For  several  lessons  past  we  have  done  nothing  new 
with  ear-training.  It  is  presumed  that  the  student  has 
been  working  quietly  alone,  reaching  toward  greater  facil- 
ity in  recognizing  the  individual  tones  of  the  chord,  and  in 
recognizing  position  and  inversion,  possibly  also  in  recog- 
nizing, or  in  making  a  beginning  in  recognizing  the 
degree  of  the  scale  upon  which  a  given  chord  is  placed. 
Specific  direction  is  scarcely  necessary  for  this  work,  and 
if  a  student  has  not  already  tried  to  do  this  it  should  now 
be  undertaken  without  further  delay. 

Next  we  should  try  to  distinguish  Dominant  seventh 
chords  from  triads,  chiefly  by  the  absence  or  the  presence 
of  repose,  elsewhere  described  as  dissonance  or  conso- 
nance. 

ir,7.  QUESTIONS. 

Answer  again  questions  14-29,  Key,  pp.  71-72. 
158.  NOTES  ON  ADVANCED  PART-WRITING. 

As  you  go  into  more  difficult  work,  you  will  find  it 
more  frequently  necessary  to  double  the  Third,  occasion- 
ally to  carry  the  Leading  Tone  downward  and  to  violate 
other  tendencies,  for  the  following  reasons: 


(Iradt'd    Lc'snons    in    Ifdrmoui/  135 

(1)  The  musicians  who  wrote  the  exercises  did  not 
definitely  understand  the  tendencies  as  a  principle.  Dr. 
Jadassohn,  for  example,  felt  the  tendencies  but  did  not 
systematize  them. 

(2)  In  general,  these  tendencies  are  not  always  para- 
mount. They  are  always  to  be  held  in  mind  and  observed 
when  there  is  a  choice ;  but  when  by  observing  them  we 
run  into  awkward  progressions  or  consecutives,  or  even 
if  the  work  cannot  be  made  as  smooth  as  otherwise,  we 
should  not  consider  tendencies  in  the  least.  In  a  word, 
they  are  to  be  observed  only  when  nothing  is  to  be  lost ; 
therefore  do  not  hesitate  to  violate  a  tendency  or  double 
the  Third  of  a  chord  when  you  think  any  improvement 
can  be  gained  thereby  which  will  outweigh  the  disadvan- 
tage of  violating  the  tendency. 


136 


Graded   Lessons    In    Ilarvionj^ 


LESSON  27. 

CADENCES:   ELABORATED 
MELODICALLY. 

Improvisation. 

159.  Note.  The  above  high-sounding  title  means  simply  that 
we  are  to  form  cadences  with  melodic  passing  notes  instead  of 
going  directly  from  the  Dominant  seventh  to  the  Tonic  chord. 
We  can  elaborate  the  progressions  in  the  several  examples 
given  below. 

KEYBOARD  EXERCISES. 

(a)  Following  the  example  given  in  Fig.  8  (a)  below, 
play  the  cadence  in  every  ]\Iajor  and  Minor  key. 

(b)  Similarly  play  the  cadences  in  all  keys,  following 
in  tone  the  examples  shown  in  Fig.  8  (b)   and  (c). 

Special  Note.     The  student  should  now  read  H.  S.,  §§315- 
322. 

Note.  The  student  should  write  three  examples  in  each  of 
the  above  mentioned  forms  as  part  of  the  lesson,  to  show  that 
he  is  doing  the  work  correctly.  He  may  also  try  to  originate 
other  forms,  more  or  less  similar  to  the  examples  shown  below 
and  may  write  illustrations  of  them.  It  is  also  well  to  look 
for  examples  of  cadences  in  printed  music,  observing  the 
habits  of  different  composers  in  this  respect,  or  comparing 
different  styles  of  music. 


Fig.  8. 

1^ 

or        .  1              N 

<> 

^> % 

if 

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• 

1              1^     • 

mJ-    _ 

;                [ 

'^    ^ 

a 

J m 

_jL — 1 

Fed.         *     P^<^' 


# 


Graded  Lessons    in    Ifarmdini 


137 


f-- 


a"=E 


:=4: 


._i — 


qnz: 


^^i=M=^ 


Ped. 


Fed. 


138  Graded  Lessons    in    Ilarmonij 


LESSON  28. 
HARMONIZING  THE  SCALE. 

160.  XOTE. 

So  much  difficulty  has  been  experienced  bj'  beginners  in 
harmonizing  the  scale  that  the  study  in  this  line  has  been 
delayed  till  now  instead  of  following  the  order  of  H.  S. 

The  student  should  realize  that  any  note  may  belong  to 
three  different  triads,  since  it  may  be  the  Root  of  one  triad, 
tlie  Third  of  another  and  the  Fifth  of  another.  For  example, 
the  note  C  is  found  in  the  triad  of  C-E-G,  of  A-C-E  and  of 
F-A-C. 

It  should  also  he  remembered  that  we  cannot  harmonize  the 
scale  by  any  promiscuous  series  of  chords  which  contain  suc- 
cessive tones  to  be  harmonized,  but  that  a  certain  natural 
succession  of  chords  is  required.  It  is  very  difficult  to  say 
what  constitutes  a  natural  or  conventional  series  of  chords. 
In  one  way  it  appears  a  little  like  the  feeling  of  gravitation 
toward  the  kev  center.  Please  read  carefully  H.  S..  §§340, 
341  :  also  /vVy.'pp.  180-183.  The  student  is  also  recommended 
to  learn  the  opening  paragraphs  of  a  most  valuable  little  work 
by  Dr.  Cutler,  "Harmonic  Analysis,"  published  by  Ditson. 

EXERCISES. 

Fill  out  the  inner  voices  in  exercises  1,  2.  3,  4.  H.  S.. 
§135  (a),  afterward  referring  to  Key  as  usual.  Next 
complete  exercises  5,  6,  7,  8  of  the  same  section;  then 
do  the  exercises  (b),  (c),  (d)  and  (f),  omitting  (e) 
unless  you  are  experienced  in  work  of  this  character. 


(iriulcd   Lessons    in    llnrmoiii/  139 

LESSON  29. 

SECONDARY  CHORDS  OF  THE  SEVENTH. 

PART-WRITING. 

101.  STATEMENT. 

There  is  a  natural  tendency  inherent  in  music,  causing 
a  common  chord  to  progress  to  the  chord  whose  root  is  a 
fifth  below  or  a  fourth  above.  This  seems  to  be  a 
natural  characteristic  of  music,  and  defies  rational  ex- 
planation. (The  writer  believes  this  to  be  the  conven- 
tional result  of  constantly  hearing  the  cadencing  close  of 
Dominant  to  Tonic ;  but  he  can  hardly  pursue  the 
thought  here.)  When  the  seventh  is  added  to  the  com- 
mon chord,  making  a  dissonance,  this  tendency  to  pro- 
gress to  the  fifth  below  or  the  fourth  above  becomes  more 
marked,  and  in  the  case  of  the  Dominant  seventh  chord 
it  is  even  more  marked  still.  Mr.  Cutler,  in  his  Harmonic 
Analysis,  says  that  following  this  thought,  the  chord  upon 
111  progresses  naturally  to  that  upon  VI,  VI  to  II,  and 
\'  to  I.  He  says  further,  that  the  nearer  this  progres- 
sion approaches  to  Tonic  harmony  the  more  gratifying 
and  reposeful  the  effect,  which  is  another  way  of  saying 
the  natural  tendencies  have  been  satisfied. 

For  the  above  reason  we  may  expect  the  secondary 
chords  of  the  seventh  to  follow,  in  a  general  way,  the 
treatment  of  the  chord  of  the  Dominant  seventh.  It 
should  be  remembered,  however,  that  as  the  tendencies  in 
the  secondary  seventh  chords  are  either  absent  entirely, 
or  are  less  in  agreement  with  each  other,  the  net  result, 
or  tendency  to  progress  to  the  chord  a  fourth  higher  or 
a  fifth  lower,  is  much  less  pronounced.  In  fact,  these 
same  tendencies,  which  were  so  unvarying  in  the  case  of 
the  Dominant  seventh  chord,  may  even  make  it  very  easy 
for  the  secondary  chords  of  the  seventh  to  progress  in 
an  irregular  manner;  so  do  not  expect  the  secondary  sev- 
enth chords  to  be  as  well  behaved  as  those  of  the  Domi- 
nant seventh.     Do  not  forget  that  the  Dominant  seventh 


140  Graded   Lessons    in    Harviovii 

is    the    one    chord    which    is    Hke    Xalurc's    Clwrd,    ami 
that  it  has  qualities  and  properties  possessed  by  no  others. 

STUDY  H.  S.,  §176-178. 

WRITTEN  EXERCISES. 

Write  the  scale  of  G  Major.  Upon  each  degree  write 
the  chord  of  the  seventh,  using  only  scale  tones — no  acci- 
dentals. Now  describe  the  first  or  Tonic  seventh  chord, 
by  naming  and  describing  each  and  every  interval,  not 
only  from  the  root  Init  from  the  other  notes  as  well,  stat- 
ing in  which  interval  or  intervals  the  chord  differs  from 
the  chord  of  the  Dominant  seventh  built  upon  the  same 
root.  Proceed  similarly  with  each  secondary  seventh 
chord. 

KEYBOARD  DRILL.     Key,  p.  93. 

162.  RESOLUTIONS. 

Statement.  As  just  stated,  the  resolution  of  these 
chords,  while  often  following  that  of  the  Dominant  sev- 
enth chord,  is  in  no  way  obligatory,  since  the  tendencies 
do  not  incline  in  the  same  way  in  all  the  chords.  In  fact, 
the  resolution  of  these  chords  is  more  like  the  progression 
of  the  triads,  and  might  well  be  called  "progression" 
instead  of  resolution.  This  brings  us  to  the  consideration 
of  the  point  that  in  music  there  are  two  ways  of  moving 
from  chord  to  chord:  (1)  by  simple  progression;  that  is, 
moving  from  chord  to  chord  as  in  connecting  triads,  either 
with  or  without  the  common  note  (see  H.  S.,  §102  ct  seq.)  ; 
(2)  by  resolution,  in  which  the  tendency  notes  point  the 
way.  (See  H.  S.,  §152  ct  scq.)  In  the  first  case  the  pro- 
gression of  the  chord  is  more  or  less  free,  as  there  is 
usually  a  choice  of  possible  chords  to  follow ;  in  the  latter 
case  the  progression  is  not  free,  but  is  practically  forced 
to  one  particular  chord  by  the  operation  of  the  tendencies. 
In  the  secondary  seventh  chords  there  are  tendencies,  of 
course,  but  as  in  very  few  cases  do  the  tendencies  of  any 
two  notes  agree,  there  is  no  real  and  positive  force  opera- 
ting in  any  one  direction.  The  fact  that  there  is  a  dis- 
sonance forces  us  to  the  conclusion  that  some  chord  must 
follow,  but  Zi'hich  chord  is  not  so  clearly  shown,  for  the 
tendencies  do  not  unite  upon  any  one.  Being  therefore 
more  free,  the  secondary  seventh  chords  may  be  treated 


(haded    T.cssoiis    in   llarmonij  141 

more  like  coninioii  chords  or  triads,  and  may  be  allowed 
to  progress  to  any  chord  of  the  key,  provided  that  for- 
bidden progressions  like  consecutive  fifths,  etc.,  are  not 
formed,  and  that  the  effect  is  good  (if  it  sounds  well  it 
will  probably  not  be  wrong,  though  of  course  what  sounds 
well  to  the  beginner  might  not  always  be  the  choice  of  the 
experienced  musician). 

COLLATERAL  READING. 

Read  H.  S.,  §§187-188.  This  will  give  a  little  further 
light  upon  the  subject. 

WRITTEN  EXERCISES. 

Form  in  turn  each  secondary  seventh  chord  (the  chord 
upon  each  degree  of  the  scale  except  the  fifth)  in  the  key 
of  C  Maj.,  and  resolve  each  one  to  as  many  different  com- 
mon chords  in  the  key  as  appear  to  you  to  sound  well, 
taking  care  to   avoid   forbidden  progressions. 

KEYBOARD  EXERCISES. 

Proceed  as  above,  using  in  turn  every  other  Major  key. 
(Advanced  students  may  do  the  same  with  the  six  Minor 
keys  also.) 

PART-WRITING,  H.  S.,  §184,  fifth  ex.  only. 


142  dradi'd   Lessons    in    Harmon  if 


LESSON  30. 

SECONDARY  SEVENTH  CHORDS— 
PART-WRITING  (Cont.) 

163.  Commence  with  the  sixth  exercise,  H.  S.,  §184. 
complete  the  exercises  in  that  section  and  in  §186. 

Analytical  and  Comparative  Reviews. 

164.  NoTK.  While  wc  are  working  steadily  forward  in  part- 
writing,  it  is  not  practicable  to  develop  further  new  principles, 
but  it  is  most  earnestly  suggested  that  this  is  the  proper  time 
to  make  a  thorough  review  of  all  the  matter  studied  up  to  this 
point.  As  you  read,  try  to  realize  the  symmetry  and  com- 
pleteness of  the  laws  of  music:  that  they  are  the  laws  of 
nature  expressed  in  this  our  chosen  form.  Try  also  to  realize 
that  the  same  laws  are  expressed  in  architecture,  in  oratory, 
in  painting,  sculpture  and  in  every  department  of  life. 

STUDY  with  great  care  H.  S..  §201,  and  Key.  201,  p. 
110.  Think  out  as  carefully  as  you  can  the  relationship 
of  each  principle  of  the  science  of  musical  structure,  and 
its  application  in  the  work  so  far  as  you  have  studied. 

STUDY  also  H.  S.,  §§202-203. 

Complete  your  review  with  this  lesson,  as  with  the 
next  lesson  we  shall  undertake  further  work  in  ear- 
traininsf. 


Graded    Lessons    in    Ilarmonij  143 


LESSON  31. 

SECONDARY  SEVENTH  CHORDS  IN 
MINOR-PART-WRITING  (Cont.) 

IGj.   study  H.   S.,  §lbT  and   write   the  exercises   there 
outlined. 

WRITTEN  EXERCISES. 

Write  the  chord  of  the  seventh  upon  the  seventh  de- 
gree of  every  Major  scale,  and  resolve  to  the  Tonic  chord. 
Write  upon  two  staves,  and  in  four  parts. 

KEYBOARD  EXERCISES. 

Repeat  the  above  at  the  keyboard,  using  t\\  o  hands. 

PART-WRITING  EXERCISES. 

H.  S.,  §§188,  189.     (Compare  with  Key.) 

Ear-training:  Dominant  Seventh  Chords. 

100.  It  is  presumed  that  the  student  has  made  some  prog- 
ress in  distinguishing  the  chord  of  the  Dominant  seventh 
from  Major  or  Minor  triads.  Assuming  this  to  be  the 
case,  we  will  now  try  to  recognize  the  various  positions  of 
the  chord  of  the  Dominant  seventh.  The  process  is  some- 
what as  follows :  Taking  as  the  basis  for  comparison  the 
individual  quality  of  scale  tones  described  in  Lesson  2.  it 
becomes  quite  simple  to  distinguish  the  position  of  the 
chord  of  the  seventh,  and  also  the  position  of  the  Tonic 
triad  to  which  it  resolves.  (Consider  the  Dominant  seventh 
chord  in  the  following  illustrations  to  be  that  of  G-B-D-F 
and  the  Tonic  chord  to  which  it  resolves.  C-E-G.)  When 
the  chord  of  the  seventh  is  in  the  position  of  the  third 
for  example  (B  at  the  top),  the  Leading  Tone  of  the  scale 
is  felt  to  be  prominent,  and  it  will  resolve  or  progress 
upward  a  half-step  and  give  a  decided  feeling  of  finality 
when  it  reaches  the  Tonic  C.     Again,  if  the   Dominant 


144  Graded   Lessons    in   Harmony 

chord  is  in  the  position  of  the  fifth  (D  at  the  top),  we 
will  feel  a  downward  tendency  in  the  upper  note,  D,  and 
a  sense  of  finality  or  completeness  when  it  goes  downward 
to  the  Tonic,  C.  If,  on  the  contrary,  D  progresses  up  to 
E  in  the  Tonic  chord,  the  incompleteness  will  be  quite 
apparent.  Again,  if  the  Dominant  seventh  chord  be  in 
the  position  of  the  seventh  (F  at  the  top),  the  tendency 
to  go  down  will  be  apparent,  but  the  result  will  not  be  final 
as  it  will  progress  down  to  the  third  of  the  Tonic  chord. 
Again,  if  the  Dominant  chord  be  in  the  position  of  the 
octave  (G  at  the  top),  it  will  not  move,  but  will  keep  the 
same  letter  in  the  resolution.  This  leaves  a  sort  of  "float- 
ing" feeling  as  contrasted  with  the  calm  incompleteness 
of  the  position  of  the  third  of  the  final  chord  and  the 
definite  close  when  the  final  chord  is  in  the  position  of  the 
octave. 

Work  out  the  above  thoroughly  at  the  keyboard,  listen- 
ing and  comparing  the  different  positions  as  described, 
then  if  necessary  write  out  these  different  positions  and 
ask  a  friend  to  play  them  in  miscellaneous  order  while 
you  are  to  judge  of'results.  In  all  the  above,  if  the  bass 
is  used  it  should  invariably  be  in  the  direct  form.  You 
will  find  this  much  less  difficult  than  you  anticipate.  The 
author  has  been  delighted  to  find  so  simple  and  compre- 
hensive a  way  of  presenting  this  subject. 

icr.  OUESTIOXS  1-27,  Key,  pi*.  Ill,  IKMU. 

168.  EXERCISES   IN   HARMONIZING  THE  SCALE. 

(a)  H.  S.,  §171; 

(b)  H.  S.,  §175.     (See  Illus.,  Key,  pp.  184-185.) 


G reded   Lessons    in    IJdimovi/  145 


LESSON  32. 

SECONDARY  SEVENTH  CHORDS— 
PART-WRITING  (Cont.) 

169.  PART-WRITIXG:     EXERCISES     WITH     XOX- 

CADEXCIXG  RESOLUTIOXS. 

After  studying  H.  S.,  §§192-195,  and  Key,  188,  107,  p. 
109,  proceed  with  the  part-writing  exercises  in  H.  S.,  §196. 

Ear-training:  Dominant  Seventh  Chords. 

170.  TO  DISTIXGUISH  THE  DIFFEREXT  IX\'ER- 
SIOXS  of  the  chord  of  the  Dominant  seventh  and  its 
resohition,  use  the  same  course  of  reasoning  for  the  Bass 
as  was  applied  to  the  upper  voice  in  the  last  lesson  on 
Ear-training.  It  is  more  difficult  than  the  preceding,  for 
the  reason  that  it  is  more  difficult  to  distinguish  the  bass 
note  and  to  separate  it  from  the  other  notes  of  the  chord. 
Those  students  who  have  been  most  faithful  in  the  pre- 
vious prescribed  drill  in  singing  the  inner  notes  (or  differ- 
ent notes)  of  the  triads,  will  be  best  prepared  for  this 
drill.  I  would  suggest  that  before  undertaking  the  dis- 
covery of  the  inversions  by  ear  it  will  be  most  desirable 
to  give  careful  drill  to  singing  the  lowest  tones  in  various 
inversions  of  the  chords  of  the  Dominant  seventh,  with 
or  without  the  assistance  of  a  friend  at  the  piano. 


146  Graded  Lessons   in   Harnwni/ 


LESSON  33. 

SECONDARY  SEVENTH  CHORDS— 
PART-WRITING  (Cont.) 

171.  STUDY  Key.  200,  p.  104. 
PART-WRITIX'G.     H.  .V.,  §2(l()  (afterward  refer  to  Key). 

Analytical  and  Comparative  Review. 

172.  Study  carefully  H.  S..  §201,  and  Key,  201,  pp.  110-111. 
Try  to  realize  how  the  various  terms,  such  as  Major, 
Minor,  Augmented,  Diminished,  Principle,  Signature,  Ten- 
dency, etc.,  have  a  systematic  application,  and  how  the 
l)rinciples  involved  follow  like  a  thread  throughout  the 
whole  subject.  It  is  this  universal  application  to  founda- 
tion principles  which  makes  this  study  so  simple,  so  scien- 
tific and  so  satisfying. 


Graded   Lessuus    in    Ilarmoni/  147 

LESSON  34. 

INTRODUCTION  TO  MODULATION. 

(NOTE.  The  following  lesson  is  designed  to  give 
facility  in  handling  chords  and  in  developing  the  con- 
sciousness of  related  ke}s,  rather  than  to  be  a  systematic 
|)resentation  of  the  subject  of  modulation.) 

173.  Definition.  Modulation  is  the  connection  of  two 
(lit^'erent  keys,  or  the  process  of  passing  from  one  key  to 
another. 

PROCESS.  There  are  a  large  number  of  ways  by 
which  modulation  can  be  effected.  In  a  later  lesson  a  defi- 
nite means  of  modulating  from  any  key  to  any  other  will 
be  given.  In  this  lesson  it  is  desired  to  show  how  easily 
we  may  progress  from  one  key  to  the  key  of  its  Dominant 
or  Sub-dominant.  It  will  be  remembered  that  the  Domi- 
nant and  Sub-dominant  are  the  nearest  related  keys  of 
any  given  key;  therefore  the  progression  to  either  of  these 
keys  occurs  more  frequently  than  to  any  others.  A  modu- 
lation may  be  effected  very  easily  where  the  two  keys 
have  a  chord  in  common ;  that  is,  a  chord  which  is  the 
same  in  both  keys.  In  such  a  case,  this  common  chord 
may  be  approached  as  if  it  belonged  to  the  first  or  old 
key,  and  may  progress  as  if  it  belonged  to  the  new  key, 
or  key  to  which  we  modulate. 

Modulation  to  the  Dominant. 

To  illustrate,  let  us  modulate  from  the  key  of  C  to  the 
key  of  G.  We  find  upon  observation  that  the  chord  of  C  is 
the  first  degree  in  the  key  of  C  and  the  fourth  degree  in  the 
key  of  G.  Therefore,  although  when  first  heard,  the  chord 
of  C  suggests,  or  may  be  said  to  ])elong  to,  the  key  of  C, 
it  may  be  followed  by  the  chords  in  the  key  of  G,  since 
it  also  belongs  to  that  key.  A  simple  way  of  modulating 
would  be,  therefore,  to  make  use  of  the  Closing  Formula, 
as  may  be  illustrated  in  the  following:  (O.  K.  stands  for 
Old  Key,  or  the  key  froiii  which  we  modulate,  and  N.  K, 
for  New  Key,  or  key  to  which  we  modulate.) 

FORMULA:   (a)   O.  K.    f    T 

N.  K.  1    IV,  L,  V,  I. 


148 


Graded    Lessons    in    Ildrmoni/ 


Illustrated  in  notes  it  would  he  as  follows  in  the  three 
positions : 

Fig.  9. 


-tz^^ 


*#= 


KeyofC  (   I 
"     "GUV 


V7 


IV 


l6 
4 


-2?- 

V7 


"tr^: 


(5"^- 


Key  of  C  (  1 
"     "  G  (IV  Ifi 

4 

WRITTEN  EXERCISES. 

Following  the  examples  in  Fig.  9,  write  examples  of 
modulations  to  the  Dominant  in  any  four  keys,  showing 
the  modulations  in  all  three  positions  in  each  key. 

KEYBOARD  EXERCISES. 

(a)  Taking  in  turn  every  Major  key.  niudulate  to  the 
key  of  the  Dominant.  Much  care  should  be  taken  with 
this  exercise ;  note  whether  it  is  easy  to  find  the  chords, 
and  with  what  speed  you  can  perform  the  modulations  in 
all  keys, 

(b)  Advanced  students  will  repeat  the  above  in  all 
INIinor  keys. 

Modulation  to  the  Sub-Dominant. 

174.  ILLUSTRATION. 

To  modulate  to  the  key  of  F  from  the  key  of  C  This 
modulation  is  also  effected  by  means  of  a  common  chord; 
for  the  chord  of  C.  which  is  the  first  degree  of  the  key  of 


(iriidcd    Li-s.s())i.s    ill    Ilarnioii  1/ 


149 


t  ,  is  also  the  chord  upon  the  fifth  degree  or  Doiumaiit  in 
tlie  key  of  F.  We  can  therefore  perform  this  modulation 
hy  simply  adding  the  Dominant  seventh  of  the  new  key. 
creating  a  cadence  in  that  new  key  as  shown  in  the  illus- 
tration below.  It  should  be  said  of  the  modulations  both 
to  the  Dominant  and  Sub-dominant,  that  in  order  to  make 
the  modulation  correct  the  rhythmic  arrangements  of  the 
chords  should  be  as  described  in  //.  S..  §1!*". 


-ez- 


7Sr 


% 


Key  of  CI  I 

"     "Ft  V 


(   I 


^^6/^- 


zs: 


V7       I 
WRIT  T  F,  X  K  X  R  R  t '  I S  E  S . 


V7 


V7 


Modulate  from  the  Tonic  to  the  .Sub-dominant  in  three 
positions,  in  any  four  Major  keys. 

KEYBO.\RD  EXERCISES. 

(a)  Take  in  turn  every  Major  key;  modulate  to  the 
key  of  the  Sub-dominant  as  shown  in  Fig.  1<>.  Xote  in 
detail  the  ease  or  difficulty  of  the  operation. 

(b)  Advanced  students  will  repeat  the  above  in  all 
Minor  keys. 

Modulation  to  the  Relative  Minor. 


17'.').  In  the  preceding  modulations  the  connection  was  ef- 
fected by  means  of  a  chord  common  to  both  keys,  followed 
by  some  form  of  the  closing  formula.  ^Modulation  to  the 
relative  Minor  may  be  effected  similarly,  since  the  Tonic 
chord  in  the  key  of  the  relative  Minor  is  identical  with 
that  upon  the  sixth  degree  of  the  key  from  which  we 
modulate. 

PROCESS.  As  the  Tonic  chord  of  the  relative  Minor 
has  a  note  in  common  with  the  old  Tonic,  we  may  pass 
directly  to  the  new  Tonic  triad;  but  this  is  not  sufficient 
to    "establish"    the    new    kev.     This    should    lie    followed. 


150 


(iraded    Lessons    in    Harmon  if 


llit-relore,  eitlier  h\  the  new  Doiiiinanl  se\eiith  chord, 
which  resolves  to  the  new  Tonic,  as  illustrated  at  (a) 
below,  or  by  a  larger  portion  of  the  closing  formula,  as 
shown  at   (b). 

NoTF..  There  are  other  and  smoother  ways  of  modulating 
to  the  relative  Minor,  but  at  present  we  are  striving  for  the 
most  simple  means  and  will  therefore  be  satisfied  even  if  the 
effect  is  not  the  most  artistic  possible. 


Fig.  11. 

or  ih) 

/ 

^   ,.- 

=i^^ 

-rf^-5- 

-s? — 

"1= 

_^_ 

.71 

SJ 

/ 

^-j 

1 

^~ 

-<&— 
^ 

f 

■5J^ 

P— ^^ 

— s?— 

-25— 





\ 

\^      a 

-z?- 



-^ — 

S)— 



-z?— ■ 

KeyofCn 
"     "A 


VI 
I 


V7 


VI 
I 


Ifi 
4 


-6>- 

Vt 


WRITTEN  EXERCISES. 

l""rom  the  same  four  keys  modulate  to  the  key  of  the 
relative  Minor,  adding  the  closing  formula  as  before. 
Each  of  these  modulations  should  be  done  in  two  or  more 
positions  and  inversions:  to  do  the  same  thing  in  several 
positions  and  inversions  stimulates  the  inventive  ability 
and  you  \vill  find  this  helpful. 

KEYBOARD  EXERCISES. 

Taking  in  turn  every  Major  key,  modulate  to  the  key 
of  the  relative  ]\Iinor.  In  every  case  try  several  inver- 
sions and  several  positions,  and  observe  which  is  the  best 
effect. 

Spixial  Note.  In  all  work  in  Modulation  special  pains 
shoukl  be  taken  to  observe  the  rules  of  part-writing.  The 
point  in  which  pupils  are  most  likely  to  violate  good  taste  are: 
(a)  Non-observance  of  Tendencies  (this  has  been  discussed 
elsewhere):  and  (b)  l-'ailure  to  treat  inverted  basses  (basses 
of  inverted  chords)  as  melodies  and  to  lead  them  stepwise 
instead  of  skipping  as  in  tlio  ordinary  Bass  (direct  form). 

Remark.  If  yon  hnd  by  comparing  your  work  with  the 
Key.   tliat   ymi    ha\e    \iolated    tendencies,    wrongly    treated    the 


(iradid    Ltxxoits    iit    /finfnoni/  151 

iiiNCiU'd  l.a-s  (ir  I'ntxx'il  I  lie  rli.iiarttT  of  tlu-  prrigi-cssioii>. 
_\(ni  will  need  a  little  review  oi  liie  ])(iiins  mentioned,  rather 
than  the  studv  uf  the  complicated  forms  of  modulation  which 
i)f  themselves  are  sufficiently  difticult  after  one  has  learned 
the  trick  of  handlin;.;  voices  properly. 

STUDY  asain  Lessons  13  and  id.  Review  witii  this  all 
the  notes  on  part-writint>  to  be  found  in  the  Key.  Also  study 
over  the  matter  of  tendencies  and  do  what  you  can  about 
applying  the  points. 

17G.  RELATR'E    SHARPNESS   OF    SCALE   TONES. 

There  is  a  wonderful  application  of  the  principle  of 
"relative  sharpness"  described  in  H.  S.,  §20.  The  prin- 
ciple is  this:  Comparing  the  relative  sharpness  of  the  dif- 
ferent notes  of  the  scale  of  C,  it  will  be  found  that  the 
letter  B  is  the  sharpest  note,  represented  by  five  sharps. 
Now  B  is  the  Leading  Tone  in  the  scale  of  C.  The  next 
sharpest  note  is  E.  with  four  sharps;  the  next  sharpest  is 
A,  with  three  sharps.  Then  comes  D,  with  two  sharps. 
(i,  with  one  sharp,  and  C,  with  no  sharps,  and  finally  F. 
with  one  flat,  or  "minus  one"  sharp. 

For  the  sake  of  illustration,  these  different  letters  in 
their  rank  of  decreasing  number  of  sharps  might  be  com- 
])ared  to  the  officers  in  a  regiment  of  soldiers.  The  com- 
mand is  held  by  the  highest  officer,  represented  by  five 
sharps,  or  B.  If  this  highest  officer  is  removed,  E  will 
become  the  highest  remaining  officer,  as  it  is  the  next  in 
order.  If  E  is  removed,  A,  with  three  sharps,  takes  com- 
mand, and  so  on  down  through  the  series,  D,  G,  C  and  F. 

Applying  this  to  the  scale,  let  us  destroy  the  rank  of 
B  by  changing  it  to  Bb.  which  leaves  E  as  the  sharpest 
note.  E  is  therefore  the  Leading  Tone  of  the  scale,  and 
the  scale  containing  Bb  is  seen  to  be  the  scale  of  F,  of 
which  E  is  the  Leading  Tone.  If  we  now  lower  E  to  Eb, 
the  next  sharpest  note  is  seen  to  be  A,  which  is  the  Lead- 
ing Tone  in  the  key  of  Bb.  Lowering  A  in  turn,  we  find 
D,  the  next  sharpest  note,  to  be  the  Leading  Tone  in  the 
key  of  Eb,  which  key  has  been  developed  by  flatting  the 
three  previous  letters  as  described.  Continuing  in  turn, 
we  find  that  the  keys  of  Ab,  Db  and  Gb  are  successively 
developed. 

It  shotdd  be  seen  that  the  list  of  keys  successively  pro- 
duced above  is  nothing  else  than  the  descending  circle  of 
kevs.     Through  this  it  mav  be  observed  that  the  key  of  C 


152  (irddcd    Lessons    in    Ihirmoiiji 

ci)it<)iiiizcs  kt-y  rt-latioiiships  in  a  still  more  wonderful 
manner  than  that  described  in  the  statement  that  the 
Dominant  and  the  Sub-dominant  keys  are  represented  in 
the  tetrachord  relationship,  and  also  in  a  more  wonderful 
manner  than  that  described  in  §40. 

WRITTEN  EXERCISE. 

Repeat   the  process,   demonstrating:   each    stei\   in   the 
keys  of  D,  E  and  Bb  ]\Iajor. 

'  READ  H.  S..  §§29.  250;  also  AVv.  p.  119. 


Cradcd   Lessons    In    Uarmonii  153 

LESSON  35. 

ATTENDANT  CHORDS.     1. 
Preparation  for  Modulation  and  Analysis. 

177.  NOTE. 

The  subject  of  Attendant  Chords  is  one  of  the  most  won- 
derful and  beautiful  features  of  these  lessons.  It  is  also  won- 
derfully simple  although  almost  universal  in  its  application, 
for  it  is  a  remarkable  and  logical  carrying  out  of  the  simple 
principles  of  relationship,  viz.,  the  relation  of  Dominant  and 
Tonic.  Remember  that  in  this  you  are  not  studying  sorne- 
thing  entirely  new  and  strange,  but  only  a  wider  application 
of  something  you  already  know. 

STUDY  H.  S.,  §§265-207. 

WRITTEN  EXERCISES. 

(a)  To  what  triad  does  the  chord  of  the  seventh  on 
G  resolve?  Write  the  chord  of  the  Dominant  seventh 
upon  two  staves  in  direct  form  and  position  of  the  sev- 
enth, and  resolve  it. 

(b)  Fill  out  the  Dominant  seventh  chord  upon  every 
(chromatic)  degree  and  resolve  each  to  the  proper  triad, 
having  regard  to  variety  in  position  and  inversion  in  the 
various  chords. 

(c)  (As  illustrated  in  H.  S.,  §267.)  What  is  the  root 
of  the  Dominant  seventh  chord  which  shall  resolve  to 
the  triad  of  A  Major?     Write  it  and  resolve. 

Similarly,  name  the  roots  of  the  Dominant  seventh 
chord  resolved  to  the  triads  of  Db,  AS,  Dff,  Ab,  Etf.  Write 
them  and  resolve  to  both  Major  and  Minor  triads. 

KEYBOARD  EXERCISES. 

Repeat  all  of  the  above  exercises,  forming  each  chord 
at  the  keyboard  as  promptly  as  possible,  and  resolving  the 
same.     Resolve  them  also  to  Minor  triads. 


154 


(iradcd    Lessons    in    Ildimon  1/ 


178.  STUDY  AND  THINK  ABOUT  H.  S.,  §§2(VJ-2?U 

N.B.  Remember  that  these  two  paragraphs  contain 
the  essence  of  one  of  the  greatest  principles  of  music. 
Read  to  the  end  of  the  chapter,  then  return  to  these  two 
sections  and  think  them  over  carefully  again. 

STUDY  Chapter  XII,  Key.  pp.  142-145. 

WRITTEN  EXERCISES. 

Take  the  key  of  G;  name  the  root  of  the  [A]  of  the 
Dominant.  Write  the  signature  of  the  key  of  G ;  write  the 
above  [A]  chord  and  resolve  it  to  the  Dominant. 

Repeat  the  above  process  with  the  chord  leading  to 
Super-tonic. 

Repeat  the  above  process  with  the  chord  leading  to 
Mediant. 

Repeat  the  above  process  with  the  chord  leading  to 
Sub-dominant. 

Repeat  the  above  process  with  the  chord  leading  to 
Sub-mediant. 

KEYBOARD  EXERCISES. 

Repeat  the  above  in  all  IMajor  keys  and  carefully  note 
your  success — whether  you  find  it  confusing  to  keep  two 
chords  in  mind  in  addition  to  the  key.  whether  you  have 
difficulty  in  instantly  forming  the  required  chords  and  re- 
solving them,  and  whether  you  find  it  difficult  to  do  the 
above  in  various  positions  and  inversions. 

179.  WRITTEN  EXERCISES:  //.  S.,  §274,  (a). 

KEYBOARD  EXERCISES:  H.  S.,  §274,  (b). 

Read  H.  S.,  §275. 

Think  of  the  tremendous  bearing  of  this  principle  upon 
music,  and  begin  right  now  to  find  examples  in  the  music 
which  comes  under  your  eye  in  your  daily  life.  See, 
further,  how  this  enlargement  of  the  boundaries  of  the 
key  and  the  richness  in  material  resulting  from  this  prac- 
tice exemplify  the  freedom  and  richness  of  modern  life 
and  the  intellectual  and  spiritual  growth  of  our  time. 

ISO.  QUESTIONS  1-ir,,  Key,  pp.  14.V14(5. 


(iradcd    T.cfisoii-s    in     Ifdirtioiii/  133 

LESSON  36. 

MODULATION  (Cont.) 
Use  of  Attendant  Chords. 

181.  OBSERVATION. 

The  method  to  be  here  developed  might  be  called  a  uni- 
versal metliod,  since  by  its  use  it  becomes  possible  to  connect 
(;;;_v  two  keys,  and  this  by  one  and  the  same  method. 

STUDY  H.  S.,  §§276-280.     Read  Key,  276,  p.  147. 

REMARKS. 

(a)  The  question  may  arise,  why  use  any  [A]  chord  at 
all  when  there  is  a  common  note.  It  would  not  be  a  modu- 
lation to  connect  the  chord  of  C  Major  with  the  chord  of 
Ab  Major — that  would  be  a  jump  into  the  new  key  and  not 
a  modulation.  To  make  a  modulation  you  must  at  some  point 
or  other  form  a  cadence,  that  is,  a  Dominant  seventh  chord 
followed  by  the  Tonic  in  the  new  key.  Therefore,  if  you  can 
get  into  the  new  key  and  form  a  cadence  at  the  same  time, 
a  more  natural  feeling  is  given  than  wlien  you  jump  from  one 
key  to  the  other  by  means  of  a  common  note  without  any  f  Al 
chords  whatever. 

(b)  I  never  like  to  use  the  [A]  of  the  first  chord  in 
practical  work,  without  the  [A]  of  the  second  chord  for 
the  reason  that  it  tends  to  return  to  the  old  key ;  so  when  it 
iiiusi  be  used  it  is  better  to  put  in  the  second  fA]  chord  as 
well  since  the  latter  progresses  naturally  to  the  new  key. 

(c)  The  [A]  chord  of  the  new  key  is  really  essential  if 
either  one  is  to  be  used.  The  [Al  chord  of  the  old  key  is 
really  only  used  to  connect  the  old  Tonic  with  the  new  \A] 
chord. 

Spkcial  Xotk.  Remember  tliat  in  finding  any  desired  [Al 
chord  we  need  only  to  ask  ourselves  wliat  TcoiiUi  be  the  Domi- 
nant if  the  (given)  triad  were  the  Tonic  of  a  key.  Attendant 
chords  are  in  their  essence  Dominant  chords,  Init  as  they  are 
only  transitory,  they  do  not  perform  the  office  of  a  Dominant. 

WRTTTEX  EXERCISES:  H.  .?..  §281,  (a). 

X.P>.  If  it  takes  you  too  long  to  write  out  the  modulation 
it   shows  that   ynnr   niclhods  arc   not  quite  complete  and  that 


156  (jiddcd   Lessons    in    Ilannonji 

you  must  learn  to  think  in  the  proper  way.  it  .\oU  would 
simply  write  the  two  chords  you  desire  to  connect  upon  a 
sheet  of  paper,  placing  the  two  chords  about  four  inches  apart 
and  then  write  between  .them  their  respective  [A]  chords,  the 
common  notes  would  come  to  light  inside  of  two  minutes. 
Of  course,  to  do  this  you  must  get  your  f.\l  chords  alisolutely 
correct. 

WRITTEN  EXERCISES:  //.  S.,  §282,  (a). 

182.  STUDY  H.  S.,  §283-284. 

KEYBOARD  EXERCISES. 

Return  to  H.  S.,  §§281-282  and  try  every  exercise  there 
given  in  as  many  different  inversions  and  positions  as 
possible,  deciding  which  form  is  smoothest  and  most 
musical. 

WRITTEN  EXERCISES. 

After  deciding  upon  the  best  form  above,  write  it  out 
in  full. 

Special  Xote.  Please  stop  at  this  point  and  do  not  try  to 
make  a  complete  modulation  yet.  Before  proceeding  we  must 
see  that  our  tools  are  in  order. 

Treatment  of  Bass  in  Inverted  Chords. 

183.  When  a  Bass  is  in  an  inversion  rather  than  in  the 
direct  form,  it  is  presumed  to  be  so  for  some  melodic 
reason ;  that  is.  so  that  the  Bass  when  taken  alone  will 
sound  more  or  less  like  a  melody.  Xow  as  in  writing  a 
melody  you  would  prefer  a  smooth  progression  to  a  series 
of  meaningless  skips ;  or  as  you  would  not  choose  an 
awkward  melody  note  for  the  sake  of  filling  up  the  chord, 
but  would  instead  arrange  the  chord  to  suit  the  melody; 
so  in  the  Bass  progression,  when  once  you  take  an  inver- 
sion, you  should  treat  the  Bass  like  a  melody  and  allow 
it  to  progress  either  step-wise  or  chord-wise  (in  its  own 
chord).  Further,  when  a  Bass  is  inverted  and  allowed 
to  progress  step-wise,  you  will  find  that  the  harmonic 
and  melodic  tendencies  come  into  great  prominence  and 
must  be  considered  in  order  to  produce  a  good  effect.  For 
example,  the  Bass  of  the  chord  (see  Fig.  12)  should 
progress   as  at    (b).   not   as   at    (a).     The   Bass  note,   G, 


Graded    hcssoiis    in    II (innnii ij 


157 


being,  an  inversion,  shonld  iml  skip  to  a  new  chord,  hut 
should  ])rogrcss  step-wise.  Try  the  two  examples  and  the 
difference  in  eft'ect  will  appeal  to  you. 

In  modulation  and  improvising,  if  you  take  an  inver- 
sion and  find  it  docs  not  progress  smoothly,  it  is  better 
to  discard  the  inversion  and  try  direct  forms ;  but  remem- 
ber that  the  use  of  these  inversions,  and  the  smooth  pro- 
gressions of  the  individual  voices  produced  thereby, "are 
a  mark  of  skill  in  chord  treatment.  The  practice,  though 
at  first  difficult,  is  most  excellent  and  should  be  continued 
for  a  long  time,  both  in  writing  and  at  the  piano. 


Fig.  12. 

(a)  poor 


(b)  good 


^EEME 


184.  Before  taking  up  the  modulations  through  the  At- 
tendant chords,  it  will  be  necessary  to  gain  facility  in 
l)assing  from  a  common  chord  to  that  inversion  of  the 
Attendant  chord,  which  will  permit  of  the  smoothest 
l)rogression  in  every  I'oicc.  The  following  special  exer- 
cises will  aid  in  this  work  : 

(1)  At  the  keyboard,  play  the  chord  of  C  in  direct 
form  and  position  of  the  fifth.  Now  pass  to  the  nearest 
form  of  its  [A]  chord,  and  then  back  to  the  C  chord.  Now 
try  if  some  other  near  inversion  will  not  answer  better, 
or  nearly  as  well. 

In  doing  this  exercise  it  is  l)est  to  consider  the  Bass 
first,  noting  the  nearest  possible  place  in  the  new  chord, 
for  upon  this  will  depend  the  question  of  which  note  to 
double.  Attend  first  to  the  Bass,  then  to  the  Soprano, 
and  then  fill  in,  trying  to  avoid  doubling  undesirable  notes 
— you  know  which. 

(2)  Repeat  the  above  in  writing. 

(3)  Take  the  chord  of  C"  in  direct  form  and  ])osition 
of  the  octave  and  pass  to  the  nearest  form  of  the  [A] 
chord  and  back,  as  before.  Try  another  progression  of 
the  Bass,  if  possible. 


158  Graded  Lessons    in    Ilarmonij 

(4)  Proceed  as  before,  hut  take  the  position  of  the 
third. 

(5)  Take  the  chord  of  C  in  the  first  inversion,  and 
try  successively  the  three  positions. 

(6)  Take  the  second  inversion  and  proceed  as  l)eforc. 

(7)  Write  out  the  complete  process  as  above,  with  the 
chord  of  C. 

(8)  Start  with  each  Major  and  Minor  triad  in  turn, 
and  do  the  same  thing.  This  will  require  several  hours, 
and  should  be  spread  over  several  days.  You  need  the 
continued  association  with  this  problem  to  get  the  best 
results.  When  ease  has  been  secured  in  this  process, 
you  can  take  up  the  real  modulations  far  more  successfully. 

IN').  WRITTEN  EXERCISES. 

Harmonize  some  descending  scales  using  [.\]  chords, 
after  studying  text  and  examples  as  given  in  Key.  p.  188. 


Graded  Lessons   in   Harmony  159 


LESSON  37. 

CHORD  ANALYSIS. 

18G.  We  now  come  to  one  of  the  most  interesting  and 
profitable  features  of  our  study.  To  be  able  to  analyze 
the  chords  in  a  composition  is  to  know  that  composition 
more  intimately,  to  play  it  more  intelligently,  and  to  enjoy 
it  more  fully  than  is  otherwise  possible.  If  we  know 
which  chord  is  the  key  center,  and  know  the  natural  rela- 
tions of  other  chords  in  the  key  to  this  central  or  Tonic 
chord;  if  we  know  the  individual  character  of  the  differ- 
ent tones  of  the  scale,  and  the  differing  tone  colors  of 
musical  effects  produced  by  Major,  Minor,  Diminished 
and  Augmented  forms;  if  we  know  the  conventional  pro- 
gression of  chords  in  a  key,  leading  or  tending  toward 
the  Tonic  chord,  and  the  effects  and  meanings  of  the 
different  kinds  of  cadences;  if  we  know  the  relations  of 
different  keys  to  one  another,  and  the  meanings  and  uses 
of  consonance  and  dissonance,  or  the  Resolution  of  the 
Dominant  principle:  if  we  know  these  things,  we  shall  l)e 
able  to  read  the  composer's  thought  almost  like  an  open 
book.  It  is  intended  from  this  time  forth  to  divide  the 
work  between  three  branches:  (1)  Logical  exposition  of 
the  principles;  (2)  Construction  and  other  drill;  and  (3) 
Analysis. 

The  methods  of  chord  analysis  will  be  best  seen  by  the 
illustration  and  description  of  the  hymn  tune,  "Old  Hun- 
dred." (Note.  The  student  should  write,  at  the  places 
designated  by  figures  in  small  tyi)e,  the  Ronian  numerals 
required  to  indicate  (1)  ujion  which  degree  of  the  scale 
each  chord  is  formed,  and  (2)  whether  Major  or  Minor, 
by  using  the  cajjital  letters  for  Major  triads  and  small 
letters  for  ]\Iinor  triads.) 


160  Graded   Lessuns    in    Ilarmoiii/ 

Analysis  of  the  Hymn. 

(In  Xotatiou  Below. j 

l^'rom  the  signature  and  the  chords  (which  do  not 
contradict  the  signature)  we  may  know  that  this  composi- 
tion is  in  the  key  of  G  Major;  therefore  write  "Key  of  G" 
(the  capital  G  to  indicate  the  Major  key)  at  X.  The  first 
chord,  consisting  of  the  notes  G-B-D-G,  is  seen  to  be  the 
chord  of  G,  or  first  degree  of  the  scale  of  G,  since  these 
notes  will  form  the  intervals  of  1,  3  and  5  from  the  root  G. 
(See  Collateral  Reading,  §75,  [2];  also  §112  [3]).  Ob- 
serve that  the  doubling  of  one  note,  G,  does  not  affect  the 
character  of  the  triad.  In  analysis  it  is  a  rule  to  "strike 
out  all  duplicates  of  notes,  and  to  bring  the  notes  within 
their  smallest  possil)le  compass,"  when  finding  the  root  of 
a  chord.  This  chord  is  a  Major  triad,  and  as  its  root  is 
(i,  the  first  degree,  write  a  capital  I  over  the  small  figure 
1.  This  chord  is  then  the  Tonic  triad  (or  common 
chord),  on  the  first  degree  in  the  key  of  G.  It  may  be 
further  described  by  saying  that  it  is  in  the  "Direct  Form" 
(that  is,  it  is  not  inverted,  since  the  root  is  in  the  Bass. 
If  this  is  not  clear,  the  student  should  refer  to  H.  S.,  p.  66 
ct  seq.;  and  Key,  Chapter  IV),  and  in  the  "position  of  the 
octave,"  since  the  Soprano  or  highest  note  is  the  root  of 
its  octave.  Observe  that  the  term  inversion  (or  Direct 
Form)  relates  to  the  Bass  or  lowest  note,  while  position 
refers  to  the  highest  note,  or  Soprano.  The  second  chord 
is  a  repetition  of  the  first  chord,  and  may  be  similarly 
designated,  above  the  small  figure  2,  or  a  short  horizontal 
line  may  be  used  instead,  to  indicate  that  the  previous 
harmony  is  continued. 

The  third  chord,  by  the  process  of  excluding  duplicates, 
placing  the  notes  as  near  together  as  possible,  and  apply- 
ing the  test  to  the  intervals  forming  1,  3  and  5,  will  be 
seen  to  be  the  common  chord  or  triad  on  the  note  D. 
which  is  the  fifth  degree  of  the  scale.  This  chord  should 
be  designated  by  a  capital  V  above  the  figure  3.  Observe 
that  it  is  in  the  direct  form  (root  in  the  Bass)  and  the 
position  of  the  Third,  since  the  note  which  is  a  third 
above  the  root  (D)  is  in  the  Soprano.  Notice  that  the 
marking  of  a  chord  does  not  specify  the  position  or  inver- 
sion, but  only  its  .'ictual  root,  or  note  ni)()n  which  the  chord 
is  built. 

Proceeding   similarly,   mark   the   successive   chords   as 


Graded   Lcsnoiis    in   Ilarnwuif  161 

follows:  At  4,  a  small  vi,  as  the  chord  is  Minor;  at  5.  a 
small  iii,  as  this  chord  is  also  Minor;  at  (!,  a  small  vi 
again;  at  7,  a  capital  V;  at  8,  a  capital  I.  This  completes 
the  first  line  of  the  words.  The  next  two  measures  will 
be  quite  simple,  if  it  is  remembered  that  a  chord  is  not 
affected  by  being  spread  out  over  several  octaves,  since 
the  notes  are  considered  just  as  if  they  were  within  the 
compass  of  one  octave,  or  as  close  together  as  possible. 
Observe  this  particularly  at  chords  1-i  and  15. 

In  the  third  line  of  the  words,  chord  18  is  inverted. 
This  is  proven  by  the  fact  that  Fft  could  not  be  the  real 
root,  since  if  that  were  the  root  the  other  notes  would 
have  to  be  A  and  C,  counting  respectively  a  third  and  a 
fifth  above  Ftf ;  but  as  the  notes  given  are  A  and  D 
instead  of  A  and  C,  some  other  note  must  be  the  actual 
root.  If  we  try  first  A  and  then  D  as  a  possible  root,  we 
will  find  that  the  notes  which  are  a  third  and  a  fifth 
above  D  correspond  with  those  here  given,  proving  that 
the  root  is  D,  although  the  lowest  note  is  F*.  Now  the 
Roman  numeral  should  represent  the  real  root,  and  not 
the  note  which  may  happen  to  be  lowest;  therefore  we 
must  mark  this  chord  with  a  capital  V,  and  not  with  a 
YH,  as  might  be  supposed  at  first  glance.  Similarly, 
chord  21  is  an  inversion  of  the  Tonic  triad,  I,  and  must  be 
so  marked ;  and  chord  23  is  an  inversion  of  the  chord  on 
Fff,  and  must  therefore  be  marked  with  a  small  vii. 
(Note.  This  chord  is  a  Diminished  triad,  and  in  addition 
to  the  Minor  sign  (the  small  letters  in  its  numeral),  it 
should  have  affixed  the  sign  °,  to  show  the  Diminished 
quality ;  viz.,  vii°.) 

Chord  31,  with  the  last  quarter  note  in  the  Alto, 
presents  four  different  notes,  a  form  at  present  beyond 
us.  We  will  therefore  mark  it  by  an  interrogation  point, 
indicating  that  it  is  a  subject  for  later  study. 

If  desired,  the  position  of  each  chord  may  be  indicated 
by  the  figures,  3,  .5  and  8  placed  over  the  treble  staff,  and 
the  direct  form  or  inversions  by  the  letter  D,  or  first  or 
second  placed  under  the  bass  staff',  and  below  the  Roman 
numeral. 


162 


Graded   Lessons    in    Harmoni/ 


OLD  HUNDRED. 


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187.  EXERCISES. 

Analyze  a  number  of  simple  hymn  tunes.  Do  not  yet 
attempt  to  analyze  piano  music,  as  the  many  passing- 
notes  and  broken  chords  make  it  more  complicated. 


(Iradcd    Lcsson.s    in    Ilrirtuon  1/  163 

LESSON  38. 

CHORD  ANALYSIS   (Cont.) 

188.  Below  are  several  hvnin  tunes  for  analysis  which 
should  be  done  as  illustrated  in  Lesson  37.  All  chords 
which  are  unfamiliar  to  the  student  should  be  marked  with 
a  '■  ?",  and  in  case  they  have  not  yet  been  studied,  should 
l)e  left  for  later  discussion. 

In  cases  where  the  key  is  actually  changed,  either  !)y 
coming  to  a  pause  in  the  new  key,  or  by  continuing  in  the 
same  through  several  chords,  the  change  of  key  should 
be  noted  in  each  case,  using  a  capital  letter  to  distinguish 
a  Major  key  and  a  small  letter  for  the  Minor  key.  As 
soon  as  the  subject  of  Attendant  chords  has  been  thor- 
oughly studied,  each  Attendant  chord  should  be  noted  by 
indicating  its  relation  to  its  Tonic. 

1S9.  ANALYSIS  OF  PIANO  MUSIC. 

As  we  have  not  yet  discussed  the  subjects  of  Suspen- 
sion, Syncopation,  and  other  varieties  of  structure,  there 
may  be  a  rather  large  proportion  of  chords  which  are 
not  yet  clear  to  the  student.  All  such  chords  may  be 
marked  as  before  with  the  "  ?"  and  left  for  future  studv. 

100.  PASSIX(;-NOTES. 

As  these  occur  so  frequently  in  piano  music,  the 
student  will  carefully  read  H.  S.,  §§31.5-320  before  pro- 
ceeding to  further  study  of  analysis.  Passing-notes  mav 
lie  marked  with  the  initials  P.  N.  The  student  should 
carefully  distinguish  between  passing-notes  and  those 
melodic  passages  in  which  the  notes  are  really  parts  of 
the  chords,  such  chord  notes  not  being  marked  as  passing- 
notes. 

11)1.  MATI'RIAI.    FOR   ANALYSTS. 

For  the  first  exercise  in  analysis,  a  very  simple  piano 
composition  may  be  chosen  by  the  student,  jireferably  one 


164 


Graded   Lessons    in   Harmonij 


of  the  classics,  such  as  one  iiiuvcnicni  from  a  sonatina, 
Handel's  '"Largo,"  or  a  simple  teaching  piece  if  preferred. 
The  analysis  should  show :  first,  the  main  key  and  all  the 
subsidiary  keys;  second,  the  harmonic  structure  of  every 
passage;  third,  passing-notes;  and  fourth,  any  irregulari- 
ties in  the  chord  structure  (  for  example,  any  chords  which 
cannot  be  classified  as  coming  from  any  known  root). 
The  subject  of  form-  analysis  will  be  touched  upon  later. 
The  preferred  subjects"  for  analysis  for  this  lesson  are 
one  or  two  movements  from  a  Kuhlau  or  Clementi  sona- 
tina, or  one  movement  from  the  simpler  sonatas  of  Haydn 
and  Mozart.  When  movements  are  short,  two  or  three 
movements  should  be  analyzed. 

NOTE  FOR  THE  TEACHER. 

Examples  of  difficult  chords  which  the  student  is  unable 
to  understand  should  be  put  in  the  form  of  questions  to  be 
answered.  In  every  case  the  chord  should  be  clearly  written 
out,  together  with  the  preceding  and  following  chords,  with 
the'  signature  and  plenty  of  space  for  notes  upon  the  same. 
Until  the  student  has  completed  the  work  up  to  and  including 
foreign  chords,  it  is  impractical  to  discuss  these  chords  very 
thoroughly. 


MONKLAND. 


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166  Graded  Leu  nous   in   llarmonjj 


LESSON  39. 

CHORD  OF  THE  DOMINANT  SEVENTH 
AND  NINTH. 

(Also  called  the  chord  of  the  Dominant  ninth  and  seventh, 
or  more  simply  the  "Chord  of  the  Ninth.") 

192.  STUDY  H,  S.,  §§204-200;  Key,  204. 

KEYBOARD  EXERCISES. 

(a)  Eorm  the  chord  of  the  Dominant  seventh  in  the 
key  of  G:  add  to  this  the  Major  ninth. 

(b)  Form  similarly  the  chord  of  the  Dominant  sev- 
enth and  add  the  Major  ninth  in  all  other  Major  keys. 

(c)  Repeat  the  foregoing  exercises  in  one  process, 
that  is,  strike  the  whole  chord  at  once,  without  stopping 
to  form  the  chord  of  the  seventh  and  then  adding  the 
ninth.     Continue  this  practice  until  facility  is  gained. 

193.  WRITTEN  EXERCISES. 

(a)  Write  the  chord  of  the  Dominant  ninth  in  the 
key  of  G  Major.  Describe  in  detail  each  and  every  disso- 
nant interval,  giving  the  specific  name  and  the  proper 
resolution  of  each.  (Note.  A  quick  way  to  do  this  is  to 
write  the  letters  of  the  interval,  one  over  the  other  like 
a  chord,  then  show  by  a  short  line  pointing  upward,  down- 
ward or  horizontally  how  each  note  resolves ;  and  then 
add  the  letter  to  which  the  resolution  is  made.)  Write 
each  dissonant  interval  separately  in  this  way.  Then 
write  the  chord  as  a  whole  and  affix  the  proper  line  to 
each  letter  showing  in  which  direction  each  note  resolves. 

(b)  Repeat  the  above  in  the  keys  of  A,  E,  B,  Eb,  Ab 
and  Db  Major. 


(i  faded    I  .f.s.sonx    in     1 1  a  rnioii  1/  Id? 

KKNBUARI)  exi<:rcis1':. 

riay  the  chord  oi  the  iJuminant  ninth  and  seventh 
in  each  and  every  Major  key;  while  holding  the  chord, 
search  for  each  dissonant  interval  and  observe  how  it 
should  resolve.  Take  time  to  do  this  work  carefully  and 
thoughtfully  as  it  has  educational  value. 

DRILL. 

Repeat  every  exercise  of  the  Major  keys  in  every 
Minor  key. 

Observe  that  the  ninth,  which  in  the  Major  key  is  a 
Major  ninth,  will  be  a  Minor  ninth  in  the  Minor  key. 
This  will  change  the  specific  names  of  some  of  the  disso- 
nant intervals.     Observe  the  changes  carefully. 

Give  special  attention  to  the  keyboard  work,  noting 
your  difficulties  for  future  attention. 

Inversions  of  the  Chord  of  the  Dominant  Ninth  and 
Seventh. 

194.  READ  H.  S.,  §208. 
WRITTEN  EXERCISES:  Key,  20S. 
KEYBOARD  DRILL:  Key,  208. 

Secondary  Chords  of  the  Seventh  and  Ninth. 

195.  READ  H.  S.,  §209. 
WRITTEN  EXERCISES :  Kev.  209. 
KEYBOARD  EXERCISES:  Key.  209. 

A    Study    in   Preparation    of    Dissonances. 

190.  STUDY  H.  S.,  §181;  also  §§302-^03. 
W  RITTEN  EXERCISES. 

(a)  How  would  you  prepare  the  chord  D-F-A-C-E 
in  the  key  of  C  (that  is.  what  chord  would  you  place 
before  it)  ?  Try  it  at  the  keyboard  and  see  if  the  effect  is 
pleasant. 


168  (traded   Lessons    in    Harmon  1/ 

(h)    Similarly  prepare  and  resolve  other  secondary 
seventh  and  ninth  chords. 

197.  QUESTIOXS  1-4.  AVv.  ]).  117. 

198.  EAR-TRAIXIXC. 

It  is  perhaps  less  difficult  to  recognize  chords  of  the 
ninth  and  seventh,  for  the  reason  that  they  often  sound 
much  like  suspensions  and  are  treated  very  similarly ;  that 
is,  they  are  usually  resolved  by  letting  the  highest  note 
proceed  one  degree  downward.  Since  the  ninth  chord  has 
five  different  tones,  it  also  has  a  very  full  sound. 

If  you  have  a  friend  who  can  form  chords  of  the  ninth 
interspersed  with  triads  and  chords  of  the  seventh  (both 
secondary  and  Dominant),  it  would  be  well  to  secure  aid 
at  this  point.  If  you  have  no  such  friend,  write  out  a 
series  of  disconnected  triads,  seventh  chords  and  ninth 
chords,  and  either  ask  a  friend  to  play  them  (you  could 
mark  the  triads,  seventh  chords  and  ninth  chords  with 
some  distinguishing  marks  so  that  anyone  could  tell  you 
whether  you  hear  correctly  or  not)  or  simply  look  at  the 
chords  of  the  ninth,  trying  to  imagine  how  they  sound, 
and  then  go  to  the  keyboard  and  hear  if  they  sound  as 
you  think. 

Of  course  you  will  take  every  opportunity  to  exercise 
the  faculty  of  ear-training  when  hearing  music. 


Graded    Lessons    in    Ilarmoiiii  169 

LESSON  40. 

CHORD  OF  THE  DIMINISHED  SEVENTH. 

199.  STATEMENT. 

In  this  system,  the  following  chords  are  shown  to  be 
nothing  more  than  slightly  varying  forms  of  one  and  the 
same  harmony,  viz.,  Dominant  harmony: 

(1)  The  Dominant  Seventh  chord; 

(2)  The  chord  of  the  Dominant  Major  Ninth; 

(3)  The  chord  of  the  Dominant  Minor  Ninth; 

(4)  The  chord  of  the  Diminished  Seventh ; 

(5)  The  chord  of  the  Augmented  Six-five-three; 
(G)  The  chord  of  the  Augmented  Six-four-three; 
(7)   The  chord  of  the  Augmented  Six-three. 

All  these  chords  will  be  shown  to  have  the  same  root. 
the  same  dissonant  intervals  (varying  slightly,  of  course, 
with  the  increased  number  of  notes),  the  same  tendencies 
and  the  same  resolutions.  In  thus  proving  their  similarity 
the  simplicity  of  the  subject  is  shown  in  a  more  striking 
way  than  ever  before  in  the  whole  history  of  musical 
theory.  In  the  following  lessons  the  student  should  not 
look  for  new  things  or  principles,  but  only  for  the  wider 
application  of  the  principles  developed  in  the  study  of  the 
chord  of  the  Dominant  seventh. 

STUDY  H.  S.,  §§210,  188,  211. 
WRITTEN  EXERCISES:  H.  S..  §212. 
KEYBOARD  EXERCISES:  //.  S..  §212. 

200.  STUDY  H.  S.,  §213. 

KEYBOARD  EXERCISES:  //.  S.,  §2U. 

201.  STUDY  H.  S..  §21.5.     Key.  2ir>. 
ADDITIONAL  EXERCISES:  Key.  21.-.. 


170  (iradcd    Lr.s.sons    in    II ttrmon ji 

W  KITTEN  EXERCISES. 

Complete  the  illustration  which  i.s  cuiimitiiccd  in  //.  S., 
p.  133,  Fig.  G8. 

Inversions  of  the  Chord  of  the  Diminished  Seventh. 

202.  STUDY  H.  S.,  §216. 

WRITTEN  EXERCISES:  H.  S.,  §21(;.  (a). 
KEYBOARD  EXERCISES:  H.  S..  §210,  (a).  ' 

203.  STUDY  very  carefully  and  repeatedly  //.  S.,  §§217- 
218. 

WRITTEN  EXERCISES:  //.  5.,  §219,  (b),  (c).  (d). 
KEYBOARD  EXERCISES:  H.  S..  ^219,    (b),    (c). 
(fl). 

204.  STUDY  H.  S.,  §219,  (c). 

WRITTEN  EXERCISES:  H.  S.,  §219,  (f). 
KEYBOARD  EXERCISES:  H.  S.,  §219,  (g). 

205.  ADDITIONAL  EXERCISES :  Key,  219. 
KEYBOARD  DRILL:  Key.  219. 
EXERCISES:  AVv,  219. 


(traded   Lc.snoiis    in    1 1 tirmoii  ii  171 


LESSON  41. 

CHORD  OF  THE  DIMINISHED  SEVENTH 

(Cont.) 

Study  of  Roots  and  Notation. 

206.  STATEMENT. 

The  exercise  in  Lesson  40,  calling  for  the  completion 
of  Eig.  C)8  of  H.  S.,  showed  that  although  there  are  in 
notation  twelve  different  chords  of  the  Diminished  sev- 
enth— or  even  more  by  enharmonic  writing — there  are  upon 
the  keyboard  only  three  different  forms  of  the  chord: 
namely,  those  shown  under  1,  2  and  3  of  each  section  in 
Eig.  C)S.  It  should  now  be  observed  that  the  difference  in 
these  chords,  that  is,  the  difference  between  1  under  {W) 
and  1  under  (X)  is  really  only  different  in  notation.  To 
understand  this  more  fully,  this  lesson  will  be  devoted  to 
the  study  of  roots  and  notation. 

STUDY  H.  S.,  §§238-243,  observing  particularly  the 
definition  of  the  word  "fundamental." 

WRITTEN  EXERCISES:  H.  S.,  §240;  work  es- 
pecially on  the  Diminished  seventh  chord. 

207.  WRITTEN  EXERCISES. 

(a)  Take  the  chord  B-D-F-Ab  and  re-write  the  chord 
so  that  it  shall  belong  to  and  resolve  in  the  four  dififerent 
keys  to  which  it  may  directly  belong. 

(b)  Take  the  chord  C-D#-F#-A  and  re-write  it  so  that 
it  shall  belong  to  and  resolve  in  the  four  different  keys  to 
which  it  may  belong. 

(c)  Proceed  similarly  with  the  chord  of  C$-E-G-Bb. 

KEYBOARD  EXERCISES. 

Play  the  chord  B-D-F-Ab,  and  by  (mentally)  changing 
the  notation,  or  what  amounts  to  the  same  thing,  by  men- 
tally changing  the  root,  resolve  it  directly  in  the  four 
different  wavs  above  described. 


172  Graded   Lessons    in    Ilarinonii 

OBSERX'ATIOXS. 

Please  work  very  slowly  and  carefully  upon  this  lesson, 
for  it  is  one  of  the  most  important  subjects  in  our  whole 
course. 

2<>S.  STUDY  H.  S.,  §§244-248. 

WRITTEN   EXERCISES:  H.  S.,  §248. 
STUDY  H.  S.,  §§249-251. 

To  Discover  the  Key  in  Which  a  Foreign 
Fundamental  Chord  is  Written. 

2U9.   STUDY  H.  S..  §29;  also  §§18-22  of  Hou'  to  Modu- 
late; H.  S..  §252 :  and  Key,  215. 

WRITTEN  EXERCISES:  H.  S..  §253. 

210.  STUDY  H.  S.,  §§254-257. 

211.  XOTES  AXD  OBSERVATIOXS. 

Referring  to  Lesson  2,  the  student  should  read  care- 
fully the  observations  made  upon  the  '"Office  of  the  Half- 
step."  We  are  here  to  use  a  remarkable  illustration  of 
the  same  subject.  In  the  chord  of  the  Diminished  seventh 
the  notes  lie  at  an  equal  distance  apart  (all  ]Minor  thirds), 
and  therefore  the  chord  gives  us  nothing  pointing  directly 
to  any  particular  key;  in  fact  it  may  belong  directly  to 
any  one  of  the  four  keys  by  simply  changing  its  notation, 
and  in  reality  may  pass  almost  directly  into  any  one  of 
the  twelve  ]\fajor'and  twelve  Minor  keys,  as  will  be  de- 
scribed later.  Xow  please  observe  that  if  the  missing 
root  of  any  Diminished  seventh  chord  be  restored,  the 
chord  will  no  longer  contain  exclusively  Minor  triads, 
for  the  root  will  produce,  with  the  next  tone  above,  the 
interval  of  a  Major  third.  Xow  remember  that  between 
the  Dominant  and  the  Leading  Tone  in  any  Dominant 
harmonv  the  third  is  ]^Iajor  (this  is  accomplished  in 
Minor  through  the  use  of  the  accidental  raising  of  the 
seventh  degree).  In  the  case  of  the  Diminished  seventh 
chord  without  its  root,  this  Major  third  is  missing,  and 
therefore  the  element  of  contrast  with  the  series  of  Minor 
thirds,    found   in   the   complete   chord,    is   lacking,     Xow 


Graded   Lc.isons    in    Ilarmoni/  173 

observe  further  that  the  full  chuid  from  which  the  Diniiu- 
ished  chord  is  derived  is,  of  course,  the  Minor  ninth 
chord,  and  that  the  Minor  ninth  is  naturally  just  a  half- 
step  above  the  octave  from  the  root ;  and  note  also  that 
in  the  chord  of  the  Diminished  seventh,  this  Minor  ninth 
is  present  and  the  root  is  absent.  Therefore  if  we  were 
to  lower  the  Minor  ninth  a  half-step,  the  result  would 
be  actually  to  destroy  the  ninth  and  to  substitute  the  root 
for  it  (which  in  reality  changes  the  chord  of  the  Dimin- 
ished seventh  to  that  of  the  Dominant  seventh).  Xow 
let  us  take  the  chord  of  the  Diminished  seventh, 
B-D-F-Ab ;  if  we  either  mentally  or  actually  lower  any 
one  of  these  tones  a  half-step  we  really  introduce  the  root 
of  the  chord,  and  both  the  key  and  the  resolution  become 
instantly  clear.  For  example,  if  we  lower  B  to  Bb  the 
chord  will  belong  to  and  resolve  to  Eb.  If  instead  we  lower 
D  to  Db  (it  now  becomes  necessary  to  enharmonically 
change  B  to  Cb,  to  rnake  alternate  letters  or  thirds  from 
the  root),  Db  now  becomes  the  Dominant  of  the  key  Gb, 
and  the  chord  will  resolve  to  Gb.  Or  if  we  lower  F  to  E 
(enharmonically  change  Ab  to  GJf  to  keep  alternate  letters 
from  E).  the  chord  is  seen  to  belong  to  the  key  of  A.  Or 
if  we  lower  Ab  to  G,  the  chord  belongs  to  the  key  of  C. 

KEYBOARD  EXERCISES. 

(a)  Take  the  chord  B-D-F-Ab :  "think"  the  roots  as 
above  described  and  resolve  to  each  of  the  four  keys  in 
turn. 

(b)  Proceed  similarly  with  the  two  remaining  forms 
of  the  chord  (C-Eb-Gb-Bbb  and  C*-E-G-Bb.) 

WRITTEN  EXERCISES. 

Write  all  that  you  have  done  in  the  foregoing  keyboard 
exercises. 

To    Proceed    from    the    Chord    of    the    Diminished 

Seventh  to  Any  One  of  the  Twelve  Major 

and  Twelve  Minor  Keys. 

2\2.  STATEMENT. 

"S'ou  have  just  learned  bow  the  chord  of  the  Diminished 
seventh  may  resolve  directly  to  any  one  of  four  different 
keys.  Now  in  resolving  the  chord,  the  triad  to  which  it 
resolves  mav  be  considered  not  only  as  the  Tonic  of  the 


174  Graded  Lessons   in   Harmonii 

key,  but  it  may  also  be  a  Sub-dominant  or  a  Dominant  of 
other  keys.  In  fact  it  may  belong  to  any  key  in  which 
that  chord  could  be  found.  For  example.  B-D-F-Ab  re- 
solves directly  to  C-E-G;  C-E-G  is  the  Tonic  of  the  key 
of  C,  Dominant  in  the  key  of  F  and  Sub-dominant  in  the 
key  of  G.  By  applying  your  knowledge  of  the  closing 
formula  you  can  therefore  resolve  the  chord  B-D-F-Ab 
to  the  triad  of  C  Major;  and  you  may  either  pause  there 
or  continue  in  the  closing  formula  to  the  chord  of  either 
F  or  G  as  a  Tonic.  We  now  have  a  group  of  three  keys 
to  which  this  first  form  of  the  chord  may  be  resolved, 
namely  the  keys  of  C,  F  and  G. 

Taking  the  next  inversion  of  the  same  chord  with  one 
letter  enharmonically  changed  (D-F-Ab-Cb).  you  will 
realize  how  this  form  resolves  directly  to  the  triad  upon 
Eb ;  and  the  triad  of  Eb  may  belong  to  the  key  of  either 
Eb,  Ab  or  Bb,  as  Tonic,  Dominant  or  Sub-dominant,  re- 
spectively. Continuing  in  this  way.  it  will  be  seen  that 
the  chord  of  the  Diminished  seventh  B-D-F-Ab  may  be 
resolved  to  each  one  of  the  twelve  Major  and  twelve 
Minor  keys. 

WRITTEN  EXERCISES. 

(a)  Resolve,  as  above,  the  chord  of  the  Diminished 
seventh  B-D-F-Ab  to  each  one  of  the  twelve  Major  and 
twelve  Minor  keys. 

(b)  Similarly  resolve  the  chord  C-Eb-Xjb-A  to  each 
of  the  twelve  Major  and  twelve  Minor  keys. 

(c)  Resolve  the  chord  of  the  Diminished  seventh 
Ci^-E-G-Bb  to  each  of  the  twelve  Major  and  twelve  Minor 
kevs. 


Graded    Lessons    in    Harmon j/  175 

LESSON   42. 

CHORD  OF  THE  DIMINISHED  SEVENTH 

(Cont.) 

213.  NOTE  TO  THE  TEACHER. 

In  this  lesson  it  is  advisable  to  discuss  all  difficulties.  The 
work  is  all  a  matter  of  principles,  and  by  callino-  the  student's 
attention  to  the  great  principles,  you  may  be  enabled  to  find 
his  difficulties  very  easily.  Make  an  extended  analysis  of  the 
Keyboard  Drill  and  note  what  facility  each  one  is  gaining  by 
faithful  practice. 

PART-WRITING  EXERCISES:  H.  S.,  §220.  (Com- 
pare with  Key.) 

214.  QUESTIONS  1-15,  Key,  pp.  125-120. 

215.  HARMONIZING  THE  SCALE. 

If  not  found  too  difficult,  try  to  harnionize  a  few 
scales  in  different  keys,  using  any  of  the  chords  which 
have  been  studied  up  to  this  point.  See  Key.  p.  186,  for 
examples.     (See  H.  S.,  §221.) 


176  Graded  Lessons   in   Harmony 

LESSON  43. 

CHORDS  OF  THE  AUGMENTED  SIXTH. 

We  have  now  reached  those  very  important  but 
largely  misunderstood  chords,  those  of  the  Augmented 
sixth.  If  the  student  would  take  the  trouble  to  read  the 
treatment  of  these  chords  by  the  older  authors  such  as 
Jadassohn.  Richter,  Paul  and  others,  and  then  carefully 
study  the  exposition  here  given,  he  would  rejoice  that  he 
lives  in  the  present  age. 

The  Augmented  Six-three  Chord. 

21G.  The  student  is  advised  to  read  the  demonstrations  of 
these  chords  with  one  hand  upon  the  keyboard,  playing 
each  form  and  illustration  as  given. 

STUDY  H.  S.,  §§222-225. 

EXERCISES :  H.  S.,  §225. 

The  Augmented  Six-four-three  Chord. 

217.  STUDY  H.  S.,  §226. 
EXERCISES:  H.  S.,  §226,   (a)  and  (b). 

The  Augmented  Six-five-three  Chord. 

218.  STUDY  H.  S..  §227. 
EXERCISES:  H.  S.,  §227. 

219.  STUDY  H.  S.,  §228. 

Special  Note.     Review  and  compare  very  carefully  chap- 
ters 5-10.  as  advised  in  JI.  S.,  §228. 

220.  PART-WRITIXG   EXERCISICS. 

Three   exercises    onlv,    //.    .V.,    §2;!2.      (Compare   witli 
Krv.) 


Graded  Lessons   in   Ilarmoni/  177 

LESSON   44. 

AUGMENTED  SIXTH  CHORDS  (Cont.) 

NoTK.  The  student  is  earnestly  advised  to  study  what  is 
said  of  the  Augmented  sixth  chord  in  the  author's  Hoiv  to 
Modulate,  where  it  is  discussed  more  fully,  and  the  reasons 
for  its   former  misunderstanding  shown. 

Having  studied  the  Attendant  chords,  and  having  realized 
that  any  Attendant  chord  may  appear  in  as  many  forms  as 
there  are  forms  of  Dominant  harmony  (read  carefully  the 
N.B.,  in  H.  S.,  end  of  §228),  the  pupil  will  now  realize  that 
Attendant  chords  may  also  appear  in  the  form  of  the  Aug- 
mented sixth  chords.  It  is  one  of  these  Attendant  chords  m 
the  form  of  the  Augmented  sixth  which  confused  the  older 
theorists  as  described  below. 

Chord  of  the  Augmented  Sixth  Derived  from  the 
Supertonic. 

221.  STUDY  H.  S.,  §§229-230. 
EXERCISES  :  H.  S.,  §231  (a),  (b). 
PART-WRITING  EXERCISES :  The  last  four  exercises 

in  H.  S.,  §232. 

222.  STUDY  H.  S.,  §233. 

EXERCISES. 

Form  chords  of  the  Augmented  sixth  upon  the  Super- 
tonic,  and  resolve  them  to  the  Tonic  six-four  as  described 
above,  and  progress  to  the  Dominant  chord. 

223.  EXERCISES. 

Harmonize  the  scale  as  required  in  H.  S.,  §233.  See 
Key,  p.  186  for  example  and  read  text.  Study  examples 
as  given  in  Key,  p.  187. 

224.  EXERCISES :  H.  S.,  §234. 
SYNOPSIS. 

Write  synopsis  of  this  chapter  and  also  of  the  develop- 


178  Graded  Lessons   in   Harmony 

ment  of  the  various  chords  from  a  fundamental  tone,  as 
shown  in  H.  S.,  §235.  Try  to  do  this  without  reference 
to  the  book,  after  reading  that  synopsis  through  once. 
Read  Key,  235. 

RECAPITULATION :    H.  S..  §235.     This  is  most  im 
portant  for  the  student  who  is  able  to  think. 

Special  Note.  Try  and  realize  the  contents  of  //.  S.. 
§§236-237,  and  express  your  ideas  regarding  the  same  in 
writing.     Read  Key,  235-236,  p.  131. 

225.  QUESTIONS  1-13,  Key,  pp.  132-133. 


Graded  Lessons   in   Ilannonif  179 

LESSON   45. 

MODULATION  (Cont.) 

226.  The  modulations  so  far  made  were  incomplete, 
as  they  fail  to  give  a  complete  feeling  of  rest  in  the  new 
key.  This  feeling  of  rest  and  finality  is  secured  by  the 
addition  of  the  Closing  Formula  already  described,  and 
further  illustrated  in  H.  S.,  §289. 

EXERCISES. 

(1)  Returning  to  the  exercises  in  modulation,  Lessons 
34  and  36,  complete  each  modulation  there  made  by  the 
addition  of  the  Closing  Formula.  This  work  should  be 
largely  done  at  the  keyboard.  Three  or  four  examples, 
showing  a  variety  of  positions  and  inversions,  should  be 
written  as  a  part  of  this  lesson. 

(2)  Modulate  from  each  Major  key  to  the  key  of  its 
relative  Minor,  adding  the  Closing  Formula  in  each  case. 
Write  at  least  six  examples. 

Note.  The  larger  part  of  the  work  in  modulation  should 
be  done  at  the  keyboard,  trying  each  modulation  in  every  pos- 
sible position  and  inversion,  comparing  the  different  forms 
until  the  best  and  smoothest  progression  is  found. 

NOTE  TO  TEACHERS. 

Pupils  should  write  out  in  notation  questions  concerning 
troublesome  points,  leaving  room  for  notes  and  corrections. 
At  this  time  ample  drill  is  required  upon  each  individual  point; 
for  this  reason  this  lesson  is  limited  in  its  extent. 


180  Graded  Lessons   in  llarmonif 

LESSON   46. 

MODULATION  (Cont.) 

227.  By  reading  H.  S.,  §§290-293,  we  find  that  each 
triad  excepting  that  upon  the  seventh  degree  may  become 
a  door  through  which  the  new  key  may  be  introduced. 
The  chief  door  of  approach  (the  front  door,  so  to  speak) 
of  the  new  key  is  the  chord  of  the  Dominant,  since  it 
leads  directly  to  the  point  of  rest.  We  may  also,  as  just 
said,  enter  by  other  doors,  using,  if  desired,  one  of  the 
triads  of  the  Closing  Formula ;  but  this  method  is  less 
direct,  since  we  need  to  follow  out  the  Closing  Formula  to 
its  end  in  order  to  fully  fix  the  new  key.  However,  when 
we  wish  to  hide  a  modulation  so  that  it  will  not  be  too 
apparent  to  the  listener,  one  of  these  less  direct  chords  is 
often  chosen  as  the  means  of -entering  the  new  key.  Care- 
ful study  of  H.  S.,  §§293  and  300,  will  teach  us  how  to 
introduce  the  new  key  through  these  different  triads. 

EXERCISES. 

(1)  Study  H.  S.,  §294.  Construct  the  formula  and 
modulate  from  every  key  to  every  other  through  the  chord 
of  the  Dominant  seventh  to  the  new  key.  Try  each 
modulation  in  its  various  positions  and  inversions  and 
write  out  with  the  formula  at  least  ten  examples.  In  all 
cases  the  Closing  Formula  should  be  included. 

(2)  Modulate  from  every  key  to  every  other,  entering 
the  new  key  through  its  Sub-dominant  triad,  and  continue 
from  this  Sub-dominant  through  the  chords  of  the  Closing 
Formula  to  the  final  Tonic.     Write  out  the  formula. 

Example.  jModulate  from  C  to  A  through  the  new  Sub- 
dominant.  That  is,  pass  from  the  chord  C  to  the  chord  of 
D  (Sub-dominant  of  A)  just  as  if  you  were  modulating  to 
the  key  of  D ;  but  instead  of  stopping  on  D,  use  it  as  IV  of 
the  new  key,  and  continue  to  V-V?-!  in  the  key  of  A.  To 
illustrate: 


Graded  Lessons   in  Harmony  181 

Fig.  13. 


g 


I  [A]  of  IV  IV  l6  V7  I 

l__l  L_i i —J 

O.K.  N.  K. 

Repeat  this  in  the  other  two  positions, 

(3)  Modulate  as  above  from  every  key  to  every  other, 
entering  the  new  key  through  the  triad  upon  the  second 
degree. 

(4)  Modulate  as  above,  entering  the  new  key  through 
the  triad  upon  the  sixth  degree. 

As  it  is  possible  to  enter  the  new  key  through  any  one 
of  its  different  triads,  so  it  is  possible  to  leave  the  old 
key  by  any  one  of  its  triads;  for  example,  instead  of 
starting  directly  from  the  old  Tonic,  we  may  first  pass 
to  any  other  triad  of  the  old  key  (excepting  the  one  upon 
the  seventh  degree),  and  starting  from  that  point,  by  the 
use  of  Attendant  chords,  enter  the  new  key  through  any 
one  of  its  triads.  It  will  thus  be  seen  what  an  infinite 
variety  in  modulation  is  opened  to  the  composer ;  and 
further  it  will  be  seen  that  all  these  varieties  can  be 
formulated  and  applied  in  any  key.  To  the  writer's 
knowledge  this  is  the  first  successful  attempt  to  formulate 
the  principles  of  modulation  and  apply  them  on  a  large 
scale. 

(5)  Modulate  from  each  of  six  keys  to  other  keys, 
leaving  the  old  key  through  the  chord  of  the  Sub-domi- 
nant; next,  leave  the  old  key  through  the  triad  upon  the 
sixth  degree ;  then  leave  the  old  key  through  the  other 
triads  in  turn.  Write  out  a  few  examples  of  these  modu- 
lations, giving  the  formula  for  modulation  in  each  case, 
and  adding  the  Closing  Formula. 


182  Graded  Lessons   in   Harmony 


LESSON  47. 

MODULATION  (Cont.) 

228.  As  we  have  now  studied  the  chord  of  the  Dimin- 
ished seventh  and  the  Augmented  sixth  chords,  we  should 
put  this  knowledge  to  practical  use  in  modulation.  It  will 
be  recognized  that  as  forms  of  Dominant  harmony,  the 
chord  of  the  Diminished  seventh  or  any  of  the  chords 
of  the  Augmented  sixth  may  be  freely  used  instead  of  the 
Dominant  seventh  chord,  wherever  an  Attendant  chord 
is  required.  This  gives  us  a  still  larger  scope  of  material 
and  progression  than  was  available  when  confining  our- 
selves to  the  chord  of  the  Dominant  seventh  alone. 

EXERCISES. 

(1)  After  studying  H.  S.,  §300,  modulate  from  every 
key  to  every  other  key,  using  the  chord  of  the  Diminished 
seventh  instead  of  the  Dominant  seventh  chord  as  At- 
tendant chord.  Write  ten  examples,  giving  the  chords 
variety  of  position. 

(2)  Modulate  from  every  key  to  every  other  key,  using 
one  of  the  chords  of  the  Augmented  sixth  as  an  Attendant 
chord.     Write  ten  examples. 

229.  QUESTIONS  1-16,  Key,  pp.  147-148. 

230.  OTHER  MEANS  OF  MODULATION. 

Several  other  means  of  modulation  are  in  common  use ; 
e.g.,  modulation  by  means  of  the  common  chord,  without 
the  use  of  a  Dominant  seventh  or  Attendant  chord;  or  by 
the  use  of  the  single  common  note  which  is  used  as  a 
connecting  link  between  two  unrelated  triads.  Both  these 
methods  work  only  in  a  chance,  haphazard  way,  and  it 
is  impossible  to  formulate  their  use  into  a  method  of 
procedure  which  will  apply  in  every  case,  as  we  are  able 
to  do  with  the  Attendant  chords.  Other  illustrations  and 
further  discussion  of  artistic  modulation  may  be  found  in 
the  writer's  Hozir  to  Modulate,  to  which  the  earnest  student 
is  referred. 


Graded   Lessons    iu    Harmony  183 

LESSON   48. 
ALTERED  CHORDS. 

231.  NOTE. 

We  have  now  discussed  all  of  the  Fundamental  chords 
and  have  found  that,  practically,  there  is  but  one  Fiiiidanirntal 
chord,  which  appears  in  larger  or  smaller  forms.  It  should 
not  be  imagined,  however,  that  composers  conhne  themselves 
to  these  chords  alone,  for  they  frequently  use  combmations 
of  notes  which  fail  to  agree  in  every  particular  with  any 
chord  we  have  studied,  and  in  some  cases  they  may  even  use 
combinations  of  notes  not  traceable  to  any  particular  root. 
The  treatment  of  these  altered  notes  and  of  the  chords  in 
which  they  are  contained  is  considered  in  Chapter  XI  of 
H.  S. 

STUDY  H.  S.,  §§238-239. 

EXERCISES  :  H.  S.,  §240. 

232.  STUDY  H.  S.,  §§241-252. 
EXERCISES:  H.  S.,  §253. 

233.  STUDY  H.  S.,  §§254-257. 

EXERCISES  as  required  in  H.  S.,  §257. 

PART-WRITING  EXERCISES:  the  f^rst  five  exer- 
cises in  H.  S.,  §258.     (Use  Key  in  usual  way.) 

234.  QUESTIONS  1-7,  Key,  p.  140. 


184  Graded  Lessons   in   Harmony 


LESSON   49. 
ALTERED   CHORDS  (Cont.) 

235.  PART-WRITIXG  EXERCISES. 
The  last  six  exercises  in  H.  S.,  §258. 

236.  STUDY  H.  S.,  §§259-262. 
EXERCISES  :  H.  S.,  §263. 

Special  Note.  Read  H.  S.,  §265  very  carefully.  Try  and 
realize  its  tremendous  meaning,  and  that  the  conclusion 
reached  is  only  the  natural  following  out  and  application  of 
the  principle  of  tendencies  which  was  first  studied  at  the 
heginning  of  this  work. 

237.  QUESTIONS. 

(1)  If  a  chord  consists  of  three  Minor  thirds,  one 
above  the  other,  what  is  the  chord? 

(2)  What  Altered  chords  are  most  commonly  in  use? 

(3)  How  can  you  distinguish  between  Altered  chords 
and  Foreign  Fundamental  chords? 

(4)  What  is  the  tendency  of  Altered  chords? 

(5)  What  is  the  tendency  of  the  Minor  ninth  in  the 
chord  ? 

(6)  When  a  chord  might  be  either  a  Fundamental 
chord  or  an  Altered  chord,  how  can  its  classification  be 
determined? 

(7)  Should  Altered  tones  be  doubled? 

(8)  What  do  you  understand  by  the  Neapolitan  Sixth 
chord  ? 

QUESTIONS  8-20,  Key,  pp.  140-141. 


Graded   Lessons    in    Ilarmonij 


185 


LESSON   50. 

PASSING-NOTES. 

238.  EXERCISES. 

(1)  Following  the  example  given  below,  connect  the 
chord  of  C  with  the  chord  of  F  in  three  positions,  using 
diatonic  Passing-notes  in  one  or  more  voices. 


Fig.  14. 

Passing-note. 


Chromatic  Passing-note. 


Passing-note. 


(2)  Repeat  in  various  positions  and  inversions. 

(3)  Similarly  connect  the  chord  of  C  with  the  chord 
of  E  Minor  in  various  positions  and  inversions,  using 
diatonic  Passing-notes  in  one  or  more  voices. 

(4)  Continue  the  above  drill,  giving  six  more  exam- 
ples of  triad  connections,  preferably  using  the  simpler 
triads. 

(5)  Connect  the  triad  on  C  with  the  triad  on  G,  em- 
ploying chromatic  Passing-notes  in  one  voice. 

(G)   Repeat  in  various  positions  and  inversions. 
(7)   Give  six  more  examples  of  triad  connections  with 
chromatic  Passing-notes  in  one  voice. 


186  Graded  Lessons   in   Haimony 


LESSON  51. 

PASSING-NOTES  (Cont.) 

•239.  STUDY  H.  S.,  §§315-316. 
EXERCISES. 

(a)  H.  S.,  §317,  (a)  and  (b). 

(b)  Try  to  make  an  original  series  of  chords  (like 
Closing  Formula,  for  example),  and  insert  as  many  Pass- 
ing-notes as  possible  in  all  voices.  This  exercise  may  be 
done  either  by  making  the  straight  chords  (without 
Passing-notes)  first,  and  then  adding  the  Passing-notes; 
or  the  Passing-notes  may  enter  into  the  original  thought. 
The  composer  would  work  in  the  latter  way. 

240.  READ  Key,  pp.  180-181. 
EXERCISES. 

Harmonize  the  scale  as  in  H.  S.,  §317.  Write  several 
examples.     (See  Key,  pp.  190-191.) 

241.  STUDY  H.  S.,  §§318-319. 
EXERCISES. 

(a)  Construct  an  original  example  of  Passing- 
chords. 

(b)  Construct  a  short  phrase  with  Chromatically 
Altered  notes. 

242.  STUDY  H.  S.,  §§320-322. 
EXERCISES :  H.  S.,  §322. 

243.  STUDY  H.  S.,  §323. 

EXERCISES.  Construct  original  examples  of  In- 
verted Pedal. 

PART-WRITING  EXERCISES:  H.  S.,  §324.  (Com- 
pare with  Key.) 

244.  STUDY  repeatedly  H.  S.,  §§325-327. 

245.  QUESTIONS  1-12,  Key.  pp.  163-164. 

246.  GENERAL    RECAPITULATION:    Key,    pp.    164- 
165. 


Graded  Lessons   in   Ilcrnnuiii/  187 


LESSON  52. 

SUSPENSIONS. 

247.  This  study  is  the  beginning-  of  the  consideration 
of  how  variety  of  musical  structure  is  secured. 
STUDY  H.  S.,  §§301-304. 

EXERCISES:  H.  S.,  §305,  (a),  (b)  and  (c). 
PART-WRITING:  H.  S.,  §306.   (Compare  with  Key.) 


188  Graded  Lessons   in   Ilormontj 


LESSON  53. 

SUSPENSIONS  (Cont.) 

248.  STUDY  H.  S.,  §307. 

PART-WRITING   EXERCISES:    four   exercises    as 
in  H.  S.,  §308.     (Use  Key  as  directed.) 

249.  STUDY  H.  S.,  §309. 
EXERCISES:  H.  S.,  §311. 


Graded   Lessons    in    Ilarmonij  189 


LESSON  54. 

SUSPENSIONS    (Cont.) 

250.  PART-WRITING  EXERCISES:  last  five  exercises, 
H.  S.,  §308. 

251.  STUDY  H.  S.,  §312. 
EXERCISES:  H.  S.,  §313. 

252.  STUDY  H.  S.,  §314. 
EXERCISES. 

Try  to  find  examples  of  Syncopation;  also  of  Retarda- 
tion and  Anticipation,  in  printed  mnsic. 

253.  QUESTIONS  1-11,  Key.  p.  159. 


190  Graded  Lessons   in  Ilarmonj/ 

LESSON  55. 

CHORD  ANALYSIS  (Cont.) 

254.  Having  now  studied  the  Attendant  chords,  the 
chords  of  the  Augmented  sixth  and  the  Altered  chords, 
the  student  is  prepared  to  analyze  a  large  portion  of  more 
difficult  chords.  He  has  learned  that  the  root  of  any 
Fundamental  chord  may  be  discovered  by  means  of  the 
principle  of  the  "sharpest  note."  He  has  learned  that  this 
"sharpest  note"  is  a  sure  guide  in  the  chords  of  the  Domi- 
nant seventh.  Diminished  seventh,  Major  and  Minor 
ninth,  and  the  three  forms  of  the  Augmented  sixth ;  that 
therefore,  in  any  change  of  key  the  ruling  foreign  chord 
(the  one  usually  coming  just  before  a  cadence)  is  sure  to 
reveal  the  key,  since  almost  unfailingly  one  of  these  forms 
of  the  Dominant  chord  will  appear.  The  student  has  also 
learned  to  distinguish  between  Fundamental  chords  and 
Altered  chords. 

EXERCISES. 

The  pupil  will  now  analyze  the  whole  of  Mendelssohn's 
"Spring  Song,''  taking  as  a  guide,  if  he  wishes,  the  illus- 
tration in  H.  S.,  Fig.  80.  He  will  also  analyze  selections 
of  his  own  from  Beethoven,  including  the  more  difficult 
portions. 


Graded  Lcusons   in   Harmony  191 

LESSON  56. 

MISCELLANEOUS. 

255.  STUDY  carefully  //.  S.,  §328. 
EXERCISES. 

Make  examples  of  Cross  Relations,  and  correct  them. 

256.  STUDY  H.  S.,  §329. 
EXERCISES. 

Make   an   example   of   the   Tritone    and   correct    it. 

257.  STUDY  H.  S.,  §330. 

CONSTRUCT  or  find  examples  of  right  and  wrong 
use  of  the  chord  of  six-four. 

258.  STUDY  carefully  H.  S.,  §331,  and  apply  the  point  in 
all  later  studies   of  analysis. 

259.  STUDY  H.  S.,  §332. 
EXERCISES. 

Turn    to    past   part-writing   exercises   and   find   all 
sequential  passages  in  the  bass. 

PART-WRITING  EXERCISES:  H.  S.,  §332.  (Fol- 
low directions  about  using  Key.) 

260.  STUDY  H.  S.,  §333. 

261.  STUDY  H.  S.,  §334. 

262.  STUDY  H.  S.,  §335. 

EXERCISES. 

Advanced  students  should  be  able  to  read  a  little  in 
C  clefs  at  least.  Those  intending  to  do  orchestral  work 
will  find  it  indispensable.  The  student  is,  therefore,  ad- 
vised to  drill  himself   in  this  work,  first  by  transposing 


192  Graded  Lessons   in  Harmony 

hymn  tunes  into  the  four  clefs,  Bass,  Tenor,  Alto  and 
Soprano,  and  by  reading  orchestral  music  in  the  same 
clefs.     Study  H.  S.,  §336. 

263.  STUDY  H.  S.,  §337. 

264.  STUDY  H.  S.,  §338. 
EXERCISES:  H.  S.,  §338. 

265.  STUDY  H.  S.,  §339. 
EXERCISES :  H.  S.,  §339. 

266.  QUESTIONS   1-11,  Key,   pp.   168-169. 


Graded   Lessons   in   Ilarmonji  193 


LESSON  57. 
HARMONIZING  MELODIES. 

267.  SPECIAL  NOTE. 

This  is  a  difficult  and  vitally  important  section,  which  must 
have  careful  and  detailed  consideration.  Do  not  be  impatient, 
therefore,  in  taking  one  point  at  a  time,  nor  work  rapidly 
through  the  exercises,  but  give  thoughtful  and  musicianly 
attention  to  each  little  point. 

STUDY  H.  S.,  §340. 

STUDY  Key,  pp.  170,  180,  181  (text  only). 

EXERCISES:  H.  S.,  §340.  Work  three  exercises. 
(Compare  with  Key.) 

268.  PROCEED  similarly  with  the  rest  of  the  exer- 
cises, H.  S.,  §340.  Do  not  consult  the  Key  till  each  group 
is  completed. 

269.  EXERCISES:  Key,   p.    17G,    Additional    Exercises, 
(a)   only. 

270.  QUESTIONS. 

(1)  To  how  many  chords  (triads)  in  the  key  may  a 
given  tone  belong? 

(2)  To  how  many  triads  out  of  the  key  may  a  given 
tone  belong? 

(3)  In  choosing  the  chords  for  harmonizing  a  melody, 
do  we  think  of  anything  beside  the  possible  chords  to 
which  each  tone  may  belong? 

(4)  When  you  see  a  certain  note  in  the  melody,  do 
you  unconsciously  associate  that  tone  with  the  triad  of 
the  same  name?  (To  illustrate,  when  you  see  G  in  the 
melody  do  you  feel  that  it  will  require  the  chord  of  G  to 
harmonize  it  ?) 

(5)  Can  you  sing  the  melody  (to  be  harmonized) 
without  playing  it? 


194  Graded  Lessons   in  Harmony 

(G)    Can  you  mentally  sing  the  melody? 

(7)  When  you  mentally  (or  audibly)  sing  the  melody, 
can  you  mentally  construct  or  imagine  the  chords  to  go 
with  the  melody  tones?  If  not  the  whole,  can  you  men- 
tally construct  shorter  series  of  chords? 

271.  ANSWERS. 

ANSWER  TO  QUESTION  (2). 

Almost  an  indefinite  number ;  it  may  belong  to : 

3  Major  triads  in  each  Major  key. 

3  ]\Iinor  triads  in  each  Major  key. 

3  Diminished  triads  in  each  IMajor  key. 

2  Major  triads  in  each  Minor  key. 

2  Minor  triads  in  each  Minor  key. 

2  Diminished  triads  in  each  Minor  key. 

1  Augmented  triad  in  each  Minor  key. 

ANSWER  TO  QUESTION  (3). 

We  should  also  think  of  the  natural  succession  of 
chords  and  their  gravitation  toward  the  Closing  Formula. 

ANSWER  TO  QUESTION  (4). 

To  allow  a  given  note  to  suggest  the  chord  of  the 
same  name  is  a  common  habit  which  should  be  developed 
as  rapidly  as  possible  into  more  musicianly  ways. 


Graded  Lessons    in   Harmon  if  195 

LESSON   58. 

HARMONIZING  MELODIES   (Cont.) 

272.  SPECIAL  NOTE. 

Make  a  special  note  of  each  dirficully  you  enciuinter  in 
preparing  this  lesson. 

STUDY  Key,  pp.  180,  ISl  (repeated  from  Lesson  57). 

273.  STUDY  Key,  pp.  182,  183. 

EXERCISES  :  //.  S.,  §§341,  342  (two  exercises  only). 

274.  EXERCISES:  Key,  p.  176,  (b). 

275.  EXERCISES:  Key,  p.  176,  (f). 

276.  Examine  many  hymn  tunes  with  "choice  of 
chords"  in  mind,  noting  what  the  composer  did  and  how 
you  would  have  treated  the  given  melody  had  yoa  har- 
monized it. 

Think  over  and  review  the  principles  of  key  and  chord 
relations  as  developed  in  H.  S..  and  the  notes  in  the  Key, 
from  the  beginning  of  the  books. 

Reviciv  the  subject  of  Cadences. 

277.  QUESTIONS. 

(1)  In  mentally  singing  the  melody,  can  you  mentally 
CONSTRUCT  or  imagine  the  cadences? 

(2)  Can  you  perceive  the  divisions  of  the  melody  into 
phrases? 

(3)  When  two  harmonizations  of  a  given  tone  are 
possible,  what  should  control  or  influence  your  choice  ? 

(4)  What  is  the  general  principle  underlying  the  har- 
monizing of  melodies? 

(5)  Give  as  many  notes  and  directions  as  you  can 
about  the  choice  of  chords,  without  referring  again  to 
book  or  Key.  (Write  this  answer  after  doing  the  exercises 
in  notation.) 


196  Graded  Lessons   in  Harmony 

278.  ANSWERS. 

ANSWER  TO  QUESTION  (1). 

This  is  one  of  the  first  points  to  develop  as  we  study 
this  plan  of  evolving  the  harmony  and  melody  together. 

ANSWER  TO  QUESTION  (2). 

Each  phrase,  usually  of  even  length,  two  or  four  meas- 
ures, requires  some  kind  of  a  cadence ;  this  alone  will 
supply  a  good  proportion  of  the  required  chords. 

ANSWER  TO  QUESTION  (3). 

The  progression  or  relations  to  the  preceding  and  fol- 
lowing chords.  Also,  but  less  strongly,  the  principle  of 
variety. 

ANSWER  TO  QUESTION  (4). 

That  of  the  natural  sequence  of  chords  suggested  by 
the  Closing  Formula ;  this  does  not  apply  rigidly,  nor  in 
the  first  chords  of  a  phrase,  but  we  work  gradually  toward 
it  for  each  cadence. 

ANSWER  TO  QUESTION  (5). 
See  Key,  pp.  182,  183. 


Graded   Lessons    in   Harmony  197 


LESSON  59. 

HARMONIZING  MELODIES  (Cont.) 

279.  REVIEW  Inversions. 
REVIEW  Chord  Connection. 

REVIEW  Principles  of  Part-writing  (Key,  pp.  30-53). 
STUDY  Key,  pp.  182,  183   (review). 

280.  STUDY  Key,  pp.  lSO-190   (text  only). 
EXERCISES. 

(1)  H.  S.,  §342   (finish). 

(2)  H.  S.,  §343   (two  examples). 

(3)  Key,  p.  176,   (c). 

(4)  Key,  p.  176,  (f). 

(5)  Key.  p.  176,   (g). 

(6)  Transpose  the  harmonization  of  the  Creed  into 
two  other  keys   (written). 

(7)  Transpose  into  all  other  keys  at  the  keyboard. 

(8)  Harmonize  the  Creed  upon  a  different  tone. 
(Your  own  harmonization.) 

281.  QUESTIONS. 

(1)  In  harmonizing  melodies,  do  you  have  any  trouble 
with  the  details  of  chord  connection,  part-writing,  inver- 
sions, etc.?  Note  any  difficulties  in  full,  and  study  sepa- 
rately each  point. 

(2)  Can  you  use  the  "Half  Close"  easily  at  the  end 
of  any  of  the  phrases? 

(3)  Where  could  it  occur? 

(4)  How  can  you  discover  the  places  in  the  melody? 

(5)  Can  you  use  [A]  chords  easily  in  harmonizing 
melodies? 

(6)  Is  there  any  particular  way  of  deciding  about 
the  need  of  an  [A]  chord  in  harmonizing  melodies? 

(7)  Have  you  any  suggestions  as  to  when  inversions 
mav  be  used? 


198  Graded   Lessons   in   Harmony 

282.  ANSWERS. 

ANSWER  TO  QUESTION   (3). 

At  the  close  of  any  phrase  excepting  the  final  one, 
which  should  be  on  the  Tonic. 

ANSWER  TO  QUESTION  (4). 

When  the  end  of  a  phrase,  usually  two  or  four  meas- 
ures, occurs  upon  a  note  not  belonging  to  the  Tonic 
chord,  the  cadence  cannot  be  an  "Authentic"  one,  but  may 
be  a  Half  Close,  Deceptive,  Modulatory,  etc.  If  the  mel- 
ody note  in  question  belongs  to  the  Dominant  chord  of  the 
key,  it  may  easily  suggest  a  Half  Close. 

ANSWER  TO  QUESTION  (6). 

No  other  way  than  to  try  them;  and  when  the  use  of 
key  chords  alone  fails  to  give  the  smoothest  effect,  we 
should  try  them.  Sometimes  the  cadences  will  suggest 
them. 

ANSWER  TO  QUESTION  (7). 

Often  when  harmonizing  successive  scale  tones  in  the 
melody,  to  prevent  bad  consecutives.  The  frequent  use 
of  inversions  is  a  mark  of  musicianship. 


Graded   Lessons   in    Ilarmonij  199 


LESSON  60. 

HARMONIZING  MELODIES  (Cont.) 

283.  STUDY  H.  S.,  §343. 
EXERCISES. 

As  in  //.  S.,  §343,  write  three  examples  of  Single 
Chants  and  three  examples  of  Double  Chants. 

284.  STUDY  H.  S.,  §345. 
EXERCISE. 

Following  the  suggestions  here  given,  write  examples 
of  two  short  hymn  tunes  and  of  two  short  phrases  written 
in  free  form  for  the  piano.  Any  of  Mendelssohn's  "Songs 
without  Words,"  Schumann's  "Traumerei,"  or  a  slow 
movement   from  a  sonatina  will  serve  as  an  illustration. 

285.  STUDY  H.  S.,  §§34G-349. 


200  Graded  Lessons   in   Harmony 


LESSON  61. 

ANALYSIS  AND  FORM. 

286.  As  the  study  of  analysis  and  form  is  a  separate 
branch,  we  merely  touch  upon  the  subject  in  H.  S.,  in 
order  to  awaken  an  interest  in  this  most  necessary  and 
interesting  side  of  the  work. 

Study  carefully  and  thoughtfully  H.  S.,  pp.  224-235. 

EXERCISES,  as  suggested  and  outlined  in  H.  S., 
pp.  224-235. 


Graded   Lessons   in   Ilannonii  201 


The  author  has  endeavored  in  this  volume  to  lighten 
the  work  of  the  busy  teacher,  by  putting  into  graded 
lesson  form  the  contents  of  Harmony  Simplified.  If  the 
teacher,  with  its  help,  shall  be  enabled  to  present  the  sub- 
ject of  Harmony  in  a  simple  and  practical  form;  if  the 
student  shall  be  stimulated  to  an  ever-increasing  interest 
in  the  subject,  and  to  further  study  and  practice  along  the 
lines  laid  out;  if  the  earnest  seeker  after  a  thorough 
knowledge  of  Harmony  shall  gain  a  clearer  vision  of  the 
fundamental  principles  and  of  their  relation  to  universal 
laws;  if  modern  Harmony  study  shall  be  simplified,  broad- 
ened and  intensified,  and  musical  standards  raised  con- 
tinually higher:  then  the  purpose  of  this  volume  will  have 
been  attained. 


HARMONY   SIMPLIFIED 

By  F.  H.  SHEPARD 

Pages,  vii  and  242 


Price,  Cloth,  $1.25  Net 

For  an  author  who  has  devoted  the  best  thought  and  most 
intense  energy  of  a  busy  life  to  the  production  of  an  educative 
work,  there  can  hardly  be  a  greater  and  more  profound  satis- 
faction than  to  see  the  fruit  of  his  labors  fully  and  gratefully 
recognized  by  competent  authorities,  and  studied  with  real 
enthusiasm  by  teachers  and  pupils  alike.  The  Shepard  system 
of  teaching  harmony  is  not  only  "simplified"  (made  easier  of 
comprehension),  but  is  at  the  same  time  even  more  complete  and 
thoroughgoing  than  the  older  methods.  It  is,  emphatically, 
simple  and  direct.  Thorough  treatment  of  the  Scales,  Keys, 
Signatures  and  Intervals  prepares  the  pupil  to  grasp  with  ease 
the  principles  of  chord-building;  practical  work  is  insisted  upon 
from  the  outset;  the  principles  underlying  the  forms  of  prepara- 
tion and  resolution  are  presented  with  exceptional  clearness, 
this  highly  important  section  being  really  original  in  treatment 
and  showing  a  distinct  advance  over  former  presentations. 

No  music-teacher  who  has  the  proper  training  of  the  young 
at  heart  should  fail  to  read  this  work  with  careful  attention;  its 
suggestive  value  is  of  the  highest  order.  The  following  "ap- 
preciations" from  prominent  educators  bring  this  point  into 
strong  relief.  

From  Prof.  H.  C.  MACDOUGAL,  of  Wellesley  College 
"I  have  been  looking  at  your  'Harmony  Simplified,'  and  must  own  that 
I  am  surprised  at  its  uniform  excellence.  It  is  really  a  remarkable  book  when 
one  compares  it  with  the  old  .  .  .  treatises,  which  are  dry  in  their  literary 
style,  and  impossible  to  understand  without  a  teacher  at  the  elbow.  .  .  . 
To  come  down  to  particulars:  Scales  and  Intervals  are  much  clearer  than 
I  have  ever  seen  them.  .  .  .  Your  small-type  matter,  'synopses'  and 
'the  perceptive  faculties,'  are  all  most  excellent  and  epoch-making.  .  . 
Your  treatment  of  Chords  of  the  Seventh,  and  the  whole  idea  of  Tendencies 
and  Influences,  I  cannot  praise  too  highly;  if  you  had  done  nothing  more, 
your  book  would  live.  I  have,  with  college  students,  been  able  to  do  some- 
thing towards  showing  them  that  physical  and  psychological,  as  well  as  musical, 
principles  operated  both  in  the  choice  and  treatment  of  chords;  but  I  have 
never  approached   your  exhaustive  treatment.     ...     If   I   had  studied  a 


work  like  yours  when  I  began,  I  should  have  been  spared  many  years  of  grop. 
in«  for  light.  .  .  .  Nothing  but  sincere  admiration  for  what  must  be 
considered  the  leading  work  on  the  subject." 


From  A.   K.  VIRGIL 


"I  am  more  than  pleased  with  the  work.  It  is  perfectly  clear — truth  is 
always  clear.  You  have  followed  educational  principles  as  has  never  before, 
to  my  knowledge,  been  done  in  any  work  on  harmony.  I  am  much  interested 
in  what  you  do  in  the  book,  and  particularly  in  the  very  sensible  way  you  go 
about  it.     You  are  unquestionably  an  educator." 


From  WILLIAM  MASON 
"A  cursory  examination  has  excited  my  interest  and  produced  a  most 
favorable  impression." 

From  HOMER  A.  NORRIS 
(Author  of  "Practical  Harmony  on  a  French  Basis") 
"Your  'Harmony  Simplified'  has  so  much  to  recommend  itself  to  me  that  I 
am  constrained  to  send  you  aline  regarding  it.  .  .  .  I  have  about  decided 
to  have  my  teachers  use  your  work  in  connection  with  their  piano  lessons, 
my  own  book  being  too  difficult  for  children,  or  for  use  in  connection  with 
lessons  on  the  pianoforte." 


From  FREDERICK  ELMER  CHAPMAN 
(Director  of  Music,  Public  Schools,  Cambridge,  Mass.) 
"In  introducing  the  subject  of  Harmony  into  the  Cambridge  High  School 
course  I  have  used  no  book,  but  have  taken  my  system  from  seven  or  eight 
authorities,  yours  among  the  others.     I  have  concluded  that  it  may  be  best  to 
adopt  your  'Harmony  Simplified'  for  use  with  the  students.     ...     I  like 
your  book  very  much,  and  shall  be  glad  to  get  your  idea  as  to  its  use  in  just 
the  place  I  propose  to  use  it." 
[Note. — ^"Harmony  Simplified"  was  adopted.] 


From  "A  TEACHER' 


"I  never  expected  to  find,  nor  did  I  believe  there  was  so  much  light  on 
this  subject,  as  you  have  given  me  in  this  course." 


From  "AN  AMATEUR" 
"I  presume  to  write  you  in  order  to  thank  you  for  all  the  good  'Harmony 
Simplified'  has  done  me.  .  .  .  Twice  I  had  attempted  to  study  harmony, 
and  twice  was  obliged  to  give  it  up  in  despair  at  its  being  too  complicated.  .  .  . 
Your  book  was  a  revelation  to  me.  ...  I  had  the  comfort  of  learning  that 
the  subject  is  learnable — indeed,  most  beautifully  simple.  I  wish  to  thank 
you  for  the  knowledge  obtained  and  the  great  comfort  derived." 

203 


A    KEY   TO 

"Harmony  Simplified" 

and    a 

CLASSROOM  MANUAL 

By  F.  H.  SHEPARD 

Pages,   vi  and   191  Price,  Cloth,  $1.25  Net 

The  remarkable  success  of  Mr.  Shepard's  unique  work, 
"Harmony  Simplified,"  has  not  merely  demonstrated  its  right 
to  exist;  the  method  has  elicited  the  warmest  encomiums  of 
prominent  educators  whose  pupils  have  been  aroused  to  genuine 
enthusiasm  over  their  harmony  tasks,  and  the  heartiest  thanks 
of  students  obliged  to  study  without  a  teacher's  guidance. 

To  complete  the  good  work  comes  this  "Key"— a  veritable 
golden  key  to  the  treasure-house  of  Harmony,  for  it  is  far  from 
being  a  mere  compilation  of  "Answers  to  Questions"  and  "Solu- 
tions of  Exercises."  It  is  a  series  of  heart-to-heart  talks  between 
teacher  and  pupil,  the  teacher  drawing  upon  his  fund  of  ripe 
pedagogical  experience  to  forestall — so  it  would  seem — every 
possible  question  or  objection  that  might  be  raised  by  the  most 
inquisitive  or  opinionated  seeker  after  harmonic  truths.  It  is 
the  outcome  of  twelve  years'  further  experience  in  the  teaching 
of  classes  and  individual  students  in  accordance  with  the  princi- 
ples of  "Harmony  Simplified." 

In  the  Preface  the  author  dedicates  the  book  to  those  who 
are  seeking  to  know  "the  reasons  why."  It  is  designed,  first, 
as  a  Key  to  the  exercises  in  "Harmony  Simplified";  second, 
as  a  guide  and  classroom  assistant  in  teaching  from  that  text 
book;  and  third,  as  offering  suggestive  and  supplementary  ma- 
terial for  those  using  other  text-books.  Students  using  the 
Manuals  of  Jadassohn  or  Richter  will  find  many  of  the  Part- 
writing  exercises  solved  in  the  "Key."  To  further  aid  the 
student,  the  choice  between  various  forms  of  chords  is  discussed, 
showing  why  one  form  is  preferred  to  another  in  the  individual 

case.  .  -^  . 

The  questions  and  answers,  appearmg.as  Notes  upon  the 
Part-writing,  are  suggestions  as  to  how  the  teacher  may  pro- 
ceed in  the  classroom.  Nothing  so  establishes  the  student  m 
his  work  as  to  be  obliged  to  tell  why  each  progression  is  made. 
Such  definite  work  soon  develops  quick  choice  and  rapid  musical 
writing.  The  "Topics  for  Discussion"  at  the  close  of  various 
chapters  will  be  found  of  value  in  the  classroom  and  for  individual 
investigation,  while  many  of  the  four  hundred  questions  are 
suited  for  use  in  examinations. 


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In  addition  to  the  Technique,  there  is  a  list  of  material  suited  to 
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BOOKS  II  AND  III  IN  PREPARATION 
Published  by  A.   AGNES   SHEPARD,   Orange,  N.  J. 

MUSIC    DOMINOES 


g  I M  P  L  E  TO  PLAY— 

Exactly  as  in  ordinary 
dominoes.  For  Kindergar- 
ten, Music  Parties,  Gifts, 
etc.  Beautifully  made  in 
Celluloid. 

Price    5  0c. 

Published  by  A.   AGNES   SHEPARD,   Orange,  N.  J. 

ARPEGGIOS  for  EVERYBODY 

By  A.  AGNES   SHEPARD 

The  most  rapid  preparation  for  .Arpeggio  Playing.     Applicable 
to  ALL  GRADES  and  to  ALL  METHODS. 

PRICE,    50c. 

Published  by  A.   AGNES   SHEPARD,  Orange,  N.  J. 

206 


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